CRWR Online Report 00-6 
 
Upscaling River Network Extractions from 
Global Digital Elevation Models 
 
by 
Mary Lear, M.S.E. 
Graduate Research Assistant 
and 
Francisco Olivera, Ph.D. 
James S. Famiglietti, Ph.D. 
David R. Maidment, Ph.D. 
Research Supervisors 
 
August 2000 
 
CENTER FOR RESEARCH IN WATER RESOURCES 
Bureau of Engineering Research ? The University of Texas at Austin 
J.J. Pickle Research Campus ? Austin, TX 78712-4497 
 
This document is available online via World Wide Web at 
http://www.crwr.utexas.edu/online.html 
 
 
 
 
 
 
 
 
 
Copyright 
by 
Mary Stockley Lear 
2000 
 
 
 
Upscaling River Network Extractions from 
Global Digital Elevation Models 
 
 
by 
Mary Stockley Lear, B.S.C.E. 
 
 
Thesis 
Presented to the Faculty of the Graduate School of  
The University of Texas at Austin 
in Partial Fulfillment  
of the Requirements 
for the Degree of  
 
Master of Science in Engineering 
 
 
 
The University of Texas at Austin 
August 2000 
 
Upscaling River Network Extractions from 
Global Digital Elevation Models  
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Approved by 
Supervising Committee: 
 
David R. Maidment 
James S. Famiglietti 
                              Francisco Olivera 
Acknowledgements 
I am thankful to have worked on this project under the guidance of 
 Jay Famiglietti, David Maidment, and Francisco Olivera. 
 Thank you, Jay, for the many opportunities that you afforded me to experience 
hydrology from the field. 
 Thank you, Dr. Maidment and Dr. Olivera, for sharing your expertise and 
resources in the world of hydrology. 
Thank you to Kwabena Asante for your insights, your time, and teaching me with 
patience. 
Thank you to Aaron Berg for making sense of helpful though foreign programs.  
Thank you to Amy Orr Lear, my mom, for your constant support and your ability 
to change batteries.  
 Thank you to Teresa Hart for inspiring adventures and to Katherine Osborne for 
your generosity of time. 
Thank you to J?na Finnd?s J?nsd?ttir, Caroline Gerwe, and Carolyn Nobel for 
keeping my priorities in order.  
 
 
 
 
 
August 2000 
Upscaling River Network Extractions from Global Digital Elevation Models  
Mary S. Lear, M.S.E. 
The University of Texas at Austin, 2000 
Co-Supervisors:  James S. Famiglietti and David R. Maidment 
 
 The representation of stream networks is an integral component of river 
transport schemes used in large-scale hydrological and climate models. However, 
the coarse resolution of the cells describing the land component of climate models 
(e.g. 2.8?) is insufficient to adequately represent river flow directions across 
continents. Hence, a methodology is required for upscaling river network 
extraction from high resolution digital elevation models (DEMs) to the lower 
resolution of the climate models to which they will be applied. In this study, an 
innovative approach for upscaling flow directions is introduced. The method 
utilizes the maximum flow accumulation, computed from the high resolution 
DEM, to determine the most realistic representation of the river network at the 
coarse resolution. The approach is original because it incorporates a projected 
mesh as the overlay for the high resolution grid and uses a unique division of the 
low resolution grid into four sub-sections. Upscaled networks for rivers of Africa 
and South America are compared with the river networks from alternative 
upscaling methods and from the fine resolution river network to determine which 
approach best represents the rivers. Example river networks are provided for the 
Niger, the Congo and the Amazon River basins. 
Table of Contents 
 Chapter 1 Introduction............................................................................................1 
1.1 Motivation................................................................................................1 
1.2 Objectives .................................................................................................6 
1.3 Material Presented ....................................................................................8 
Chapter 2 Literature Review ...................................................................................9 
2.1 Resolution Sensitivities............................................................................9 
2.2 Upscaling Algorithms.............................................................................10 
2.3 Division of Coarse Boxes .......................................................................14 
Chapter 3 Methodology.........................................................................................18 
3.1 Overview of Double Maximum Algorithm............................................18 
3.2 User Input and Coarse Mesh Generation ...............................................26 
3.2.1 Rotated Coarse Mesh .................................................................33 
3.3 Upscaling Process ..................................................................................34 
3.3.1 Algorithm Steps .........................................................................35 
3.3.2 Explanation of Flow Direction Determination ..........................43 
3.4 Downstream Box Information from Raster to Vector Format ..............48 
3.5 Sinks: Inland Catchments and the Continental Margin .........................50 
3.6 Coarse Resolution River Network .........................................................56 
Chapter 4 Results and Discussion.........................................................................60  
4.1 Double Maximum Algorithm Applications ............................................60 
4.2 Analysis of Double Maximum Algorithm..............................................66 
4.2.1 Rotated Coarse Mesh..................................................................67 
4.2.2 Flow Direction Distribution.......................................................70 
4.3 Evaluation and Comparison to Other River Networks...........................72 
4.3.1 Flow Generation Algorithm .......................................................73 
4.3.2 Manual River Networks .............................................................75 
4.3.3 Observed Data River Networks..................................................77 
4.4 Contributions .........................................................................................78 
4.4.1 Projection of Coarse Mesh .........................................................79 
4.4.2 Orientation of Coarse Mesh........................................................80 
4.4.3 Division of Coarse Boxes...........................................................80 
4.5 Limitations..............................................................................................80 
4.5.1 Suggested Solution for the Integration of Smaller Watersheds..81 
4.5.2 Suggested Solution for the Uneven Flow Direction 
Distribution ................................................................................83 
Chapter 5 Conclusions...........................................................................................84  
Appendix A  Double Maximum Algorithm ..........................................................88 
Appendix B  User's Guide to Section One ............................................................99 
Appendix C  Coarse Mesh Parameters ................................................................103 
Appendix D  Projection Parameters....................................................................106 
References ...........................................................................................................109 
Vita  ....................................................................................................................110 
 
 
 1 
INTRODUCTION 
Chapter 1 
The hydrologic cycle is a complex system requiring many disciplines for 
its study. Until fifteen years ago, land surface hydrologists worked separately 
from atmospheric and oceanic scientists, as each studied distinct parts of the 
hydrologic cycle (Eagleson, 1986). Then, the global impacts of climatic events 
like El Ni?o-Southern Oscillation and La Ni?a, produced an awareness of the 
interdisciplinary nature of the hydrologic cycle as part of the climate system. In an 
attempt to better understand the climate?s behavior, scientists from atmospheric, 
oceanic and land surface hydrology began to collaborate and to model the climate 
as a coupled system. 
1.1 MOTIVATION 
Global-scale climate models, called General Circulation Models (GCMs), 
integrate many complex algorithms that describe the physical, chemical, and 
biological processes of the climate system. The four main components of GCMs 
are the land surface, atmosphere, ocean, and ice models. In the land surface 
model, the vertical movement of water in the hydrologic cycle, precipitation and 
evaporation, is well represented. However, the horizontal movement of water, 
specifically rivers, is missing from the models. Even though rivers make up less 
 2 
than one tenth of a percent of the earth?s water, their influence on both the local 
and regional-scale climate is significant. A river network for each continent, or a 
global river network, describes the horizontal movement of water over the land 
surface. Therefore, including a global river network as input for GCMs including 
the National  is necessary in order to provide a more complete representation of 
the hydrologic cycle.  
Scale plays an important part in creating a global river network. The scale 
of GCMs, like the National Center for Atmospheric Research?s Climate System 
Model, can be 2.8125? or about 300 kilometer-sized boxes, while global digital 
elevation models (DEMs) that represent the land surface topography are available 
in 30 arc-second or 1 kilometer grids. Thus a single GCM box contains more than 
100,000 DEM cells. The translation from fine resolution DEMs to coarse 
resolution river networks is called upscaling. Geographic Information Systems 
(GIS) provide an invaluable tool to solve the upscaling problem. An algorithm 
must be developed to translate fine resolution flow direction data, derived from 
the global DEMs, to a coarse resolution river network for each continent. 
The aforementioned concept of upscaling can be described visually in 
Figures 1.1 and 1.2. River networks can be created from the fine resolution global 
DEMs, which represent the river as a sequence of DEM cells, as seen in Figure 
1.1 for West Africa including the Niger River basin. The level of detail of the 
river network from the 1-kilometer grid is appropriate when performing analysis 
 3 
on the watershed scale but it is too intensive for continental scale hydrological 
studies. Therefore, an algorithm is necessary to upscale the river hydrography 
from fine to coarse resolution for use in global scale GCMs. The algorithm 
performs a series of steps on the fine resolution DEM to determine the flow 
direction that best describes the river network in the coarser scale. The upscaled 
river network for the same section of West Africa, as seen in Figure 1.2, can be 
used as input for a GCM. 
 4 
 
Figure 1.1 Fine Resolution River Network (Blue) for West Africa Shown With 
Watershed Boundaries (Red) 
 
Figure 1.2 Coarse Resolution River Network (Blue) for West Africa Shown with 
Watershed Boundaries (Red)  
 5 
Upscaling river networks from global DEMs is not a straightforward 
process. A new upscaling algorithm was created in this research to extract a 
coarse resolution river network from a fine resolution DEM. This extraction 
required a connection between the DEM, which is in raster or grid format, and the 
river network, which is in vector or coverage format. The algorithm was written 
in Arc Macro Language (AML), the language for the GIS software, ArcInfo, 
Version 7. 
Both grids and coverages are used in the algorithm and are discussed 
extensively in this thesis. To distinguish between the raster (grid) and vector 
(coverage) formats, their definitions are given here. The raster or grid format 
describes a matrix of pixels or cells where each cell has a value. In this research, 
all grids have the same fine resolution, specifically 1-kilometer, with their pixels 
being referred to as cells. 
In contrast, vector or coverage data can represent points, lines, or 
polygons where each element is described with x and y coordinates and an 
identification number. The coverages in this thesis are line and polygon type 
coverages. For example, the river networks in the previous figures are line 
coverages and the watershed boundaries are part of a polygon coverage. A key 
component of the upscaling algorithm is a polygon coverage called a fishnet as 
seen in Figure 1.3. The fishnet is a coarse resolution rectangular mesh whose 
 6 
elements are referred to as boxes. The role of the mesh will be introduced in 
Section 3.1. 
 
Figure 1.3 Example of Polygon Coverage Called Mesh  
 
1.2 OBJECTIVES  
There were two main objectives to this research. The first objective 
involved the creation of an upscaling algorithm. The main requirement of the 
algorithm was to work in an environment conducive to both the GCM and land 
surface hydrology. A goal was to create an algorithm that best represents the flow 
of water over the land surface at large scale. The second objective was to evaluate 
the algorithm by analyzing the unique aspects of the algorithm and to compare the 
 7 
river networks to the results of 1) an upscaling algorithm by O?Donnell et al., 
(1999), 2) a manual approach to determining flow direction and 3) the 
representation of the river at fine scale. 
For the first objective, an algorithm called the double maximum method 
(DMA) was created. To satisfy the requirement, a coarse resolution mesh was 
introduced and projected from geographic coordinates of the GCMs into Lambert-
Azimuthal Equal Area projection. It is necessary to work in a projected 
environment for land surface hydrology, since the land area is preserved. A square 
mesh in geographic coordinates does not have the same land area in each cell 
because of the curvature of the meridians on the earth?s surface. Since the path 
that water follows over land is important for river length calculations and routing, 
a projected environment with x and y coordinates in meter or feet rather than 
degrees must be used for land surface hydrology. A coarse resolution mesh was 
created in geographic coordinates and then projected into the same environment 
as the fine scale DEM.  
Second, the river networks from the double maximum algorithm were 
analyzed and compared with other upscaling algorithm results. The analysis 
includes examining the effects of the orientation of the coarse resolution mesh, 
the flow direction distribution, and the division of the boxes. The river networks 
were also compared to river networks from the O?Donnell et al. algorithm, a 
 8 
manual flow direction algorithm, and observed river hydrography to see which 
method extracted the best representation of the example rivers. 
1.3 MATERIAL PRESENTED 
The chapters in this thesis will describe the innovative upscaling 
algorithms in detail. Chapter 2 gives the background for the research in 
continental scale river routing in the literature review. The procedure of the 
double maximum algorithm is provided in the Chapter 3.  Chapter 4 shows the 
algorithm?s results for watersheds from two continents and a comparison to river 
networks from other algorithms. The conclusion chapter, Chapter 5, shows a 
summary of the thesis and indicates future work.  
 9 
LITERATURE REVIEW 
Chapter 2 
Global river networks play an integral role in better representing land 
surface hydrology in general circulation models (GCMs). Including global or 
coarse scale river networks in GCMs requires the upscaling of fine resolution 
grids. There are a variety of issues related to resolution for inputs and outputs to 
their models. The issue of digital elevation model (DEM) and digital terrain 
model (DTM) resolution in hydrologic model are discussed in this literature 
review. The previous work in upscaling river networks and the methods of 
upscaling are introduced. Also, the evolution of the division of the coarse boxes is 
discussed  
2.1 RESOLUTION SENSITIVITIES  
Two main groups (Quinn et al., 1991 and Wolock and Price, 1994) studied 
the effects of DTM and DEM resolution on hydrological processes and showed 
that many are sensitive to resolution. Quinn et al. tested the predictions of the 
hillslope flow processes of TOPMODEL, a topography-based hydrologic model, 
with two DTMs, a 12.5-meter and a 50-meter resolution grid. They proved that 
the spatial patterns of the ln (a/tan? ??distribution calculated from the two DTMs 
with different resolutions produced varying results. For the ln (a/tan? ? index, a is 
 10 
the cumulative upslope area draining to a point per unit contour length and tan? ?is 
the slope angle at the drainage point. The model showed higher ln (a/tan? ? values 
with the 50-meter resolution grid which indicated larger saturated areas. 
Therefore, the loss of detail with the coarser resolution DTM did affect 
hydrologic predictions which may be important for global circulation modelers to 
understand and consider.  
Wolock and Price tested the effects of map scale and data resolution on 
the hydrologic predictions of TOPMODEL. Two DEMs with the map scale of 
1:24,000 were used with 30 and 90-meter resolutions, and a 1:250,000-scale with 
90-meter resolution was also entered into the model. Their results showed that 
both the DEM scale and resolution affected the predictions of the mean value of 
the ln (a/tan? ??distributions. The spatial distribution of ln (a/tan? ? shows where 
water pools in a watershed and indicates the depth to the water table. Specifically, 
the map scale affects both the mean of the ln (a??distribution, which characterizes 
the shape of the watershed, and the mean of the ln (1/tan? ) distribution, which 
characterizes the watershed?s slope. However, the resolution affects only the 
model predictions of the mean of the ln (a) distribution. 
2.2 UPSCALING ALGORITHMS  
Working directly with resolution issues with upscaling algorithms, three 
main approaches to extracting fine resolution river network data were created. 
 11 
One approach was defined simultaneously by Fekete et al. (1999) and Kwabena 
Asante (1998) at the University of Texas at Austin. This approach called the 
inverse method works with by using the inverse of the fine resolution flow 
accumulation grid (FAC). First, the flow direction grid (FDR) is created from the 
DEM. Since the DEM cells each have an elevation value, the direction of land 
surface flow can be determined from the DEM since water flows in the direction 
of steepest decent. Next, the FAC is created from the FDR. Each cell in the flow 
accumulation grid has the value of the upstream cells which flow to it. Therefore, 
as the river approaches its mouth, the FAC grid values increase. The inverse 
method calculates the inverse of the FAC cells or multiples them by the power of 
?1. Therefore, as the Inverse FAC approaches the mouth of the river, the values 
decrease and the water can then follow the downhill path. In other words, the 
values of the Inverse FAC resemble the values in a DEM and the Inverse FAC is a 
new fine resolution DEM.  
The upscaling occurs with the inverse method using a scale factor. The 
scale factor, decided by the user, multiplies the cell size of the inverse of the FAC 
or the new DEM to obtain the desired resolution for the output grid. A flow 
direction grid and a flow accumulation grid are created from the coarse resolution 
new DEM. Then the coarse resolution river network is generated. 
Fekete et al. illustrated the inverse method, named the WB Re-scaling 
Algorithm (WBRA), to create a 10, 15, and 30 minute resolution river network 
 12 
from a 5-minute fine resolution DEM for the Danube River basin in Europe. 
Asante?s program is published on the World Wide Web at 
http://www.ce.utexas.edu/stu/asanteko/home.html. Both algorithms have the 
flexibility of inputting any resolution fine scale DEM and any scale factor which 
will upscale the river network. The resulting river networks for both algorithm 
have many side flow directions, like stair steps, and few diagonal flow segments. 
The limitation of this method is that the flow direction for the upscaled box-like 
areas cannot easily be translated to the vector format of a GCM input.  
Francisco Olivera (1998) at the University of Texas at Austin created a 
different resampling approach which introduced the use of the fishnet, 
http://www.ce.utexas.edu/prof/olivera/CoarseFDr/coarsefdr.htm, Olivera?s 
algorithm divides the fine resolution grids with fishnet boxes, and flow direction 
of the boxes is determined by the position of the river?s exit point from each box. 
Using the fishnet to divide the grids was a helpful concept that was continued in 
the double maximum method, but the resulting coarse river networks contained 
mostly flow directions to the sides and very few in the diagonal directions. 
The third main approach to upscaling was invented by O?Donnell et al. 
(1999) and provides the most comprehensive approach to date. The algorithm also 
uses a scale factor which upscales the fine scale grids. Then each coarse scale area 
is divided into nine equal subsections. The unique part of the method is that the 
algorithm follows the river network beyond the boundary of each coarse box 
 13 
through the neighboring subsections of the bordering coarse boxes. The flow 
direction is based on which neighboring area the river mainly flows to. If the river 
just ?touches? into a neighboring area before flowing across the majority of a 
second neighboring area, then the downstream area is the second area. Figure 2.1 
shows an example of the flow direction for the Coarse Area 10. Though the river 
flows into Coarse Areas 20 and 21, the downstream area is Coarse Area 11. 
  
 
Figure 2.1 O?Donnell Coarse Areas (Black), Nine Equal Divisions (Red) and the 
Fine Resolution River Network (Blue) 
The O?Donnell algorithm produces reasonable results that require few 
manual edits. A comparison of the resulting river network from the O?Donnell 
algorithm and the double maximum algorithm is seen in Section 4.3.1 of this 
thesis. The limitation of the O?Donnell approach is that the algorithm works with 
 14 
square or rectangular boxes and cannot be projected, and the projected 
environment is important for the land surface hydrology.  
The contribution of the research presented in this thesis includes two main 
improvements to the O?Donnell approach. The first improvement is the use of 
projected coarse boxes, instead of square areas. The second improvement is 
dividing the coarse mesh boxes into four subsections. The analysis of varying 
divisions of the coarse cell showed that the four subsections yielded improved 
results to the nine subsections. 
2.3 DIVISION OF COARSE BOXES  
The uneven distribution of flow directions is not a new problem for 
hydrologists modeling rivers in digital form, but the issue did initiate an 
interesting metamorphosis of this upscaling algorithm specifically related to the 
division of the mesh boxes. The early methodology of the double maximum 
algorithm (DMA) described in this thesis included dividing the coarse boxes into 
nine equal parts which created eight sub-boxes along the edge of the main box. 
This subsection describes the changes from the nine-box division to the double 
maximum algorithm?s current four-box division. 
The methodology for determining the flow direction is similar for both the 
early and the current version of the DMAs.  For each case, the maximum flow cell 
inside of each coarse box was determined, and the placement of this cell was 
critical in making the flow direction decision. The rivers were also ?tracked? 
 15 
outside of the box by using the maximum flow cells of the secondary or dividing 
mesh. 
The difference in the earlier DMA was that not all of the rivers or 
tributaries were tracked. Of the nine sub-boxes, four of them intersect with only 
one side of another coarse box. For the maximum flow cells which were located 
in one of these sub-boxes, the flow direction which the number is associated was 
given to the box. Using the same numbering convention as the eight pour-point 
model, the four sub-boxes that share a side with just one other coarse box are 1, 4, 
16, and 64 as seen in Figure 2.2. 
For the maximum flow cells that were located in either of the sub-boxes 2, 
8, 32, or 128, the position of the secondary maximum flow cell was examined.  
The flow direction was determined by which neighboring box the secondary 
maximum flow cell was placed. The division of the earlier algorithm is shown in 
Figure 2.2 with the sub-boxes in dashed lines and numbered the same as the eight  
direction pour-point model. The example coarse box is shown as a solid line.   
  
 16 
 
Figure 2.2 An Example of the Early Division of the Coarse Mesh Boxes 
The flow direction distribution from this nine-box division displayed a 
skew towards the sides. In an attempt to achieve even flow direction distribution 
the dividing mesh was changed from dividing the boxes into nine even parts to 
making the side sub-boxes (1, 4, 16, and 64) smaller. This ?squeezing? of the sub-
boxes was conducted in a series of steps of which each one shortened the length 
of the side sub-boxes. The percentages of flow directions to the sides and corners 
remarkably stayed constant despite the length of the side sub-boxes. The 
examples of the progression of steps to decreasing the sub-box size are seen in 
Figure 2.3. The dashed lines represent the secondary dividing mesh while the box 
with the solid lines is one of the coarse mesh boxes. 
 
 17 
 
 
Figure 2.3 Two Steps in the Progression of the Squeezing the Side Sub-boxes 
Though the flow direction bias was not resolved, the squeeze progression 
ultimately led to the division of the boxes into four even sub-boxes with 
statistically similar though biased results.   
 18 
METHODOLOGY 
Chapter 3 
This chapter is divided into six main sections, with an introductory section 
and each subsequent section describing a portion of the double maximum 
algorithm for upscaling river networks. The first section provides an overview of 
the algorithm?s methods. The second section describes the user inputs and the 
files required to run the algorithm. The upscaling process of the algorithm is 
explained in the third section. The fourth section describes translating the 
upscaling information from the raster format to the vector format in order to form 
the coarse resolution river network. The fifth section provides a description of the 
steps necessary to include the sinks, the inland catchments and the continental 
margin, in the river network. The final steps for the creation of the river network 
are given in the sixth section. 
3.1 OVERVIEW OF THE DOUBLE MAXIMUM ALGORITHM 
The method for upscaling river networks from fine to coarse resolution 
described in this thesis is called the ?double maximum algorithm? (DMA). The 
main concepts of the algorithm are presented in this section and illustrated in 
Figure 3.1 with an example from a portion of the Niger River in West Africa. 
Starting with the fine resolution DEM, flow direction and flow accumulation grids 
 19 
are calculated. The flow accumulation grid, as seen in Figure 3.1a, represents the 
river as a sequence of cells where each cell has a value of the number of upstream 
cells which flow to it. Therefore, the cells in the main channel of the river have 
increasing values as they reach the mouth of the river. The fine resolution grids 
are the input portion of the algorithm. 
The framework for the coarse resolution network is the mesh, Mesh A, 
previously described in Section 1.1, which covers the area of the grids is shown in 
Figure 3.1a for the continent of Africa. The goal of the algorithm is to determine 
the flow direction that best represents the direction of the river or rivers in each of 
the Mesh A boxes. This goal is accomplished with the use of two meshes. A 
second mesh, Mesh B, with the same resolution as Mesh A is placed over the grid 
but it is offset from Mesh A by half of the length and half of the height of its 
boxes as seen in Figure 3.1a. As a result, Mesh B ?divides? the boxes of Mesh A 
into four sub-sections which is different than O?Donnell et al.?s nine subdivisions. 
 20 
 21 
 
The next series of steps introduces the approach to extracting high 
resolution hydrography information. First, both meshes are intersected with the 
edges of the grid as seen in Figure 3.1b. With the intersected meshes placed over 
the flow accumulation grid, the location where the river or stream flows from 
each mesh box is determined. This exit location is defined by the fine resolution 
cell per box with the highest flow accumulation and is called the river exit cell. 
The river exit cell is found for each box in both meshes. An example of the both 
meshes and their river exit cells is shown in Figure 3.1b. The size of the cells is 
increased for visibility in the figure.  
The boxes of Mesh B create regions where the river can be tracked after it 
exits each of the Mesh A boxes. The reason for tracking the river beyond the 
boundary of the box is to provide a better representation of the river?s direction 
after it flows from the box. Because the mesh is placed arbitrarily over the DEM, 
the river may flow through a small portion of a neighboring box in Mesh A before 
flowing across the main portion of a different neighboring box in Mesh A. In 
another case, the river may flow across the main portion of the first neighboring 
box that it encounters. With the secondary mesh, the downstream box in both 
scenarios will be the box which the river crosses a main portion of. To accomplish 
tracking the river, the position of the river exit cells for Mesh B play a key role. 
 22 
 
 23 
An example of the method in which the flow direction for the Mesh A 
boxes is determined is illustrated in Figure 3.1c. First, the quadrant of the Mesh A 
box where the river exit cell falls is noted. In this example, the river exit cell for 
Box A1 is located in its southeast quadrant. Next, the Mesh B box where the Box 
A1 river exit cell is inside of is located which is Box B1 as seen in Figure 3.1c. 
The river exit cell for the Mesh B box is located inside of a different Mesh A box 
which is the downstream box for the sample Mesh A box. The downstream box 
for Box A1 is Box A2, therefore the flow direction of Box A1 is southeast to Box 
A2. 
The same flow direction determination process is applied to each box in 
the original coarse resolution mesh. The direction for the rivers in each of the 
Mesh A boxes for Africa is shown in Figure 3.1d. The flow directions make up a 
coarse resolution river network. 
 24 
 
 25 
 
 26 
3.2 USER INPUT AND COARSE MESH GENERATION  
The double maximum algorithm (DMA) was written in Arc Macro 
Language (AML), the programming language of the GIS software, ArcInfo. The 
algorithm requires two GIS files and one text file as inputs and can be executed 
when these files and the algorithm file are located in the working directory of 
ArcInfo.  
The DMA extracts river networks from any fine resolution and upscales to 
any coarse resolution specified. The example in this thesis includes upscaling a 1-
kilometer flow direction grid to a 2.8125? x 2.8125? mesh. This coarse resolution 
was chosen with the goal of using the river network in the land component of the 
National Center for Atmosphere Research general circulation model. 
Two fine resolution grids for a continent or a large watershed are a critical 
component required to run the DMA. These are the flow direction and flow 
accumulation grids, which are extracted from the processing of a digital elevation 
model (DEM). The 1-kilometer grids described in this thesis were created from 
the GTOPO30, which is the finest resolution DEM currently available for the 
world. The DEM is available from the United States Geological Survey and can 
be downloaded from the World Wide Web at 
http://edcwww.cr.usgs.gov/glis/hyper/guide/gtopo_30. The DEM should be 
processed according to the Jenson & Dominigue (1988) method for filling 
depressions and creating flow direction (FDR) and flow accumulation (FAC) 
 27 
grids. The user is prompted to input the names of the FDR and the FAC grids. See 
Appendix B for a detailed explanation of the input requirements. The two grids 
are the only GIS files required for the algorithm. 
The other required inputs are related to the resolution of the final river 
network and its projection. The resolution of the coarse river network is decided 
by the user and is entered as a set of inputs when the algorithm is initiated. The 
algorithm generates a coarse resolution mesh, Mesh A, from the mesh parameters 
given by the user. Two main inputs must be provided to describe the coarse mesh. 
Those inputs are 1) the parameters for the mesh and 2) a projection file.  
The first input describes the orientation, resolution, placement, and size of 
the coarse mesh. The coarse resolution meshes in this thesis are 2.8125? x 2.8125? 
and are created in geographic coordinates using the generate/fishnet series of 
commands. The user is prompted to input eight parameters for the mesh. The 
recommended parameters for making a north-south oriented mesh for each 
continent are given in Appendix C. An example of the input parameters is shown 
in Table 3.1 with values for the continent of Africa. 
 28 
 
ArcInfo Prompt  User Input 
Fishnet Origin Longitude -20.00
Fishnet Origin Latitude -38.00
Y-Axis X-Coordinate -20.00
Y-Axis Y-Coordinate 32.00
Cell Length 2.8125
Cell Height 2.8125
Number of Rows 28
Number of Columns 29
  
Table 3.1 Coarse Mesh Parameters for Africa 
An important characteristic of the coarse mesh is that it extends beyond 
the border of the continent or large watershed. An example of a mesh extending 
over the land surface is shown in Figure 3.2 for the African continent. 
 29 
 
 
Figure 3.2 Geographic Coarse Mesh Overlaid on the Watersheds of Africa 
The second main input necessary for the algorithm is the projection file. 
The mesh is created in geographic coordinates and must be projected into the 
same projection as the input grids. The example in this thesis uses the Lambert-
Azimuthal Equal Areas projection for which each continent has specific latitude 
and longitude projection parameters. The origin of projection parameters is the 
United States Geological Survey Earth Resources Observation Systems Data 
Center?s Hydro1K data available for each continent from the World Wide Web at 
http://edcdaac.usgs.gov/gtopo30/hydro. The parameters are in Lambert-Azimuthal 
 30 
projection and are provided for each continent in the Appendix D. An example of 
the file for Africa is shown here in Figure 3.3. 
INPUT 
PROJECTION GEOGRAPHIC 
UNITS DD 
PARAMETERS 
OUTPUT 
PROJECTION LAMBERT_AZIMUTH 
UNITS METERS 
PARAMETERS 
6378137.00000 
20 0 0 
5 0 0 
0.0 
0.0 
END 
Figure 3.3 Projection Parameters for the ArcInfo Projection Command for Africa 
Projecting the coarse mesh is an important component of the algorithm. 
Since the working environment becomes projected, then the land area is preserved 
which is important for applications in land surface hydrology. The projected mesh 
is shown here with the projected watersheds of Africa in Figure 3.4. 
 31 
 
Figure 3.4 Projected Coarse Mesh Overlaid on the Projected Watersheds of Africa 
The following steps require no additional input by the user though their 
result plays a critical role in the upscaling portion of the algorithm. This step 
involves creating a second coarse resolution mesh, Mesh B. The algorithm uses 
the inputs provided for Mesh A to create Mesh B. Mesh B is created in the same 
resolution as Mesh A though its placement is different. Offset by one half of 
Mesh A?s length and height, Mesh B appears to divide the Mesh A boxes into 
four parts when the two coverages are overlaid. The second mesh and its division 
of the original mesh help determine the flow direction of the coarse boxes which 
is described in detail in Section 3.3. The second mesh is longer and wider than the 
 32 
original mesh by one row and one column respectively. The second mesh is also 
projected. 
Both coarse meshes are shown in Figure 3.5 with the first coarse 
resolution mesh displayed as bold dark blue lines and the second mesh shown as 
red lines. 
 
Figure 3.5 A Portion of Two Projected Coarse Meshes 
The user input for the algorithm includes only the parameters for the first 
coarse resolution mesh since the second mesh is created depending on the first. 
The names of the grids and the projection file and the first coarse resolution mesh 
characteristics are the only user-input variables. The algorithm continues to run to 
completion without any other input from the user.  
 33 
3.2.1 Rotated Coarse Mesh 
The flexibility of the DMA includes more than its ability to upscale any 
resolution of flow direction and flow accumulation grids to any coarse resolution 
river network. The DMA can also create the coarse river network in any 
orientation. Because the meshes are created with user inputs and the generate 
fishnet command includes orientation parameters, then a rotated coarse river 
network is simple to extract using the DMA. Though climate models meshes are 
usually north-south in orientation, the versatility of the algorithm allows for the 
relatively easy creation of a rotated network. As an evaluation technique to 
examine flow direction distributions, river networks were created from meshes 
with a 45? rotation and compared to the perpendicular networks. The comparison, 
discussed in Section 4.2.1, can provide an understanding of the robustness of the 
DMA. 
A few minor modifications to the algorithm are needed in order to create a 
river network with a rotated mesh. The variables for creating Mesh B in relation 
to Mesh A are changed. For a rotated river network, the position of Mesh B also 
divides Mesh A into quarters but the offset direction is different. Appendix A 
shows the code for Section One for a rotated mesh, and the User?s Guide to 
Section One describes the inputs necessary for a rotated mesh in Appendix B. 
After the meshes are created, the procedure of the algorithm is exactly the 
same regardless of mesh orientation. The complete rotated mesh for Africa and its 
watersheds are seen in Figure 3.6. 
 34 
 
Figure 3.6 Geographic Coarse Mesh Overlaid on the Watersheds of Africa 
3.3 UPSCALING PROCESS 
The critical steps of the upscaling process occur in this section of the 
algorithm. The ArcInfo commands and the grids which they form are described in 
Section 3.3.1. For clarification of the upscaling procedure, an example of how 
flow direction is determined for three different flow direction scenarios for one 
coarse box is given in Section 3.3.2. 
 35 
3.3.1. Algorithm Steps 
Once the coarse meshes have been created, the algorithm begins the 
upscaling process. As the first step of the upscaling process, the algorithm moves 
to the grid mode of ArcInfo where most of the steps in this section are performed. 
Grid is the cell-based geo-processing tool of ArcInfo and requires an analysis 
environment and cell size to be declared. The flow direction grid serves both of 
these functions. A polygon coverage called BORDER is created which covers the 
same extent as the flow direction grid. For the African continent, the BORDER 
coverage is shown in Figure 3.7. 
 
Figure 3.7 BORDER Coverage of the Flow Direction Grid Extent 
Next, the meshes, which are called PRONET and PRONET2, are each 
intersected with the BORDER coverage. This intersection is important in making 
 36 
the coarse meshes cover the same area as the grids. The intersected meshes are 
called PROJECTNET and PROJECTNET2 or Mesh A and Mesh B respectively 
and are used throughout the algorithm. Mesh A is shown in Figure 3.8 for Africa. 
 
Figure 3.8 Intersected Polygon Coverage of Coarse Mesh over Africa 
After the coverages are intersected, they are converted into grids with the 
same resolution as the DEM and input grids which are 1 square kilometer cells for 
this thesis. In other words, the coverages, PROJECTNET and PROJECTNET2, 
are converted into grids called PROJECTGRID and IDGRID. This conversion 
allows for the transfer of flow direction information between grids. In the grid 
format, more than 100,000 fine cells represent each coarse mesh box and carry the 
same coarse box identification number, which is PROJECTNET# for Mesh A. 
 37 
This identification number is key in the upscaling process, switching from high to 
low resolution.  
The conversion of the projected meshes to grids (i.e., PROJECTNET to 
PROJECTGRID) is interesting to note. Since the coarse meshes are projected, 
they are not perfect squares nor are all the boxes the same shape. The 
transformation of the mesh to the grid creates a grid which does not correspond 
exactly to the projected mesh. The fine cells along the border of the mesh boxes 
get the identification number of the box of which they are inside the majority. An 
example of the ?jagged? representation of the coarse boxes is shown as a zoomed-
in view of the border of two boxes in Figure 3.9. The jagged edge does not 
introduce any problems for the algorithm. 
 
 
 
 
 
Figure 3.9 Example of Two Boxes and Their Representation in Grid Format 
The zonalmax command is a powerful tool in transferring information 
from grid to grid and is used throughout this section in this algorithm. The flow 
accumulation grid is used in conjunction with the zonalmax command in the next 
step. The zonalmax command determines the cell with the maximum flow 
 
 38 
accumulation value for each group of fine cells in a given coarse box or with the 
same coarse box identification number. The river exit cell is located where the 
river exits the coarse box and is called the ?river exit cell?. The command is 
performed on both meshes and the new grids, MAXFAC and MAXFAC2, are 
created. The river exit cells are almost always located on outside border of the 
coarse boxes with one exception. The exception is for inland catchments, or lakes 
that do not flow to the ocean, which have the river exit cell located somewhere 
inside of a coarse box. Inland catchments will be discussed in further detail in 
Section 3.5. 
To further distinguish the river exit cell in each coarse box, a conditional 
statement follows the zonalmax command. For MAXFAC, which represents Mesh 
A, the value from the flow direction grid is assigned to the river exit cells while 
all other cells receive the value of zero. This grid is called POURPOINTS because 
the river exit cell indicates where the river or stream exits or pours from the box. 
The values of the POURPOINTS grid are taken from the eight-direction 
pourpoint model and are labeled 1, 2, 4, 8, 16, 32, 64, and 128 for East, Southeast, 
South, Southwest, West, Northwest, North, and Northeast respectively. A 
depiction of four coarse boxes with their river exit cells is shown in Figure 3.10. 
The size of the cells is exaggerated for the figures in this chapter since the actual 
cells in a view with the boxes are too small to locate. The gray numbers indicate 
the identification number of the coarse boxes. 
 39 
 
 
Figure 3.10 Example of Fine Resolution River Network in Coarse Boxes (Left); 
River Exit Cells for the Coarse Boxes (Right) 
The second mesh, Mesh B, plays an important role in the upscaling 
procedure since it ?tracks? the river once it leaves the boxes of Mesh A. The 
conditional statement following the zonalmax command for the second grid, 
MAXFAC2, which represents Mesh B, assigns the value of the first coarse box 
identification number to the river exit cell. Again, all cells that are not the river 
exit cells receive a value of zero. 
For MAXFAC2, the river exit cells are distinguished form the zero value 
cells with a conditional statement. This conditional statement for the creation of 
the POURPOINTS2 grid is a key component of the upscale process. The cells in 
POURPOINTS2 with one of the eight-direction values indicate where the river or 
stream exits each box of Mesh B. As a result, the two pourpoint grids show the 
fine resolution cell where the river exits the box for each coarse box of both 
 40 
meshes. The second mesh accounts for the name of the double maximum 
algorithm. 
For clarification, the main distinction between the two pourpoint grids is 
described here. The first pourpoint grid, POURPOINTS, contains the river exit 
cells for the grid representation of Mesh A. The values of the POURPOINTS non-
zero cells are one of the eight-direction pourpoint model numbers from 1 ? 128. 
For Mesh B, the second pourpoint grid, POURPOINTS2, contains the river exits 
cells which each have the value of the Mesh A box where it is located. In other 
words, the value of the river exit cells in the POURPOINTS2 grid is the 
downstream box for the Mesh A boxes. An example of the river exit cells for a 
portion of the Mesh A and Mesh B boxes is shown in Figure 3.11 with the fine 
scale river network. The Mesh A boxes are shown with solid black lines and their 
river cells are black. The Mesh B boxes are depicted with red dotted lines with red 
cells to mark their river exit cells. The cell value for the river exit cell in Box B60 
is A21. 
 41 
 
 
Figure 3.11 Mesh A and Mesh B Boxes, Their River Exit Cells, and Fine Scale 
River Network  
Using the zonalmax command, a grid called QUADRANT is created with 
the non-zero POURPOINTS2 cell values distributed to all of the cells within the 
Mesh B boxes. For the example in Figure 3.11, all of the cells that represent the 
Mesh B Box B60 are given the POURPOINTS2 value of A21. The helpful part of 
this distribution is that the non-zero POURPOINTS cells for Mesh A then share 
the same location as a QUADRANT cell with the downstream box information. 
For this example, since the river exit cells for boxes A10, A11, and A20 are 
located in Mesh B Box B60 whose value is A21, then the downstream box for the 
three Mesh A boxes is Box A21. 
 42 
The next command transfers the downstream box information to Mesh A. 
The QUADRANT grid cells which all have the downstream box information 
correspond with the river exit cells for Mesh A and a grid, OUTGRID, is 
generated with the downstream box information. In other words, OUTGRID is 
created with a conditional statement which each non-zero POURPOINTS cell is 
given the QUADRANT value. The QUADRANT value is equivalent to the 
downstream box of Mesh A. 
The downstream box information is then distributed to each cell in the 
coarse boxes with the use of the zonalmax command. This crucial step transfers 
the downstream box numbers to the centroids of each box, which will be useful 
since the linking the centroids of upstream and downstream boxes creates the 
river network. The zonalmax command creates the FLOWZONE grid, which is 
similar to the grid representation of the Mesh A, PROJECTNET, except that its 
values are that of the downstream box. 
The last command in Section Two of the algorithm is a maintenance step. 
The NODATA cells of the FLOWZONE grid are switched to having a value of 
zero in a grid called FLOWZONE0. The grid, FLOWZONE0, will be used in 
Section Three to continue transferring the information to the coarse resolution 
river network. 
 43 
3.3.2 Explanation of Flow Direction Determination 
In general, each box has eight neighboring boxes to which water can flow. 
This algorithm like many others allows for only one downstream box or allows 
only one flow direction to be associated with each box. Each flow direction has 
been assigned a number by Jenson and Dominigue (1988). The eight possible 
directions are shown in Figure 3.12. The directions all are in relation to the center 
boxes flow possibilities. 
 
 
Figure 3.12 Eight-Direction Pourpoint Model?s Flow Direction Values  
The position of the river exit cells or pourpoints is the most important 
factor in determining the Mesh A boxes? flow directions. Since Mesh A?s boxes 
are divided into four sections by Mesh B, the river exit cells for Mesh A each are 
located in one of its quadrants. The quadrants of Mesh A and Mesh B?s river exit 
cells are the deciding factors for the flow direction of the Mesh A. An example 
with three different locations for Mesh B river exit cells will be described in this 
section. 
 44 
For each coarse box, there are eight neighboring boxes and therefore eight 
possible directions for the flow directions. However, each river exit cell for Mesh 
A falls in just one of the quadrants that is imposed by Mesh B. Hence, for each 
quadrant there are three neighboring boxes (two with which the quadrant shares a 
border and one with which it shares a corner) and three possible flow directions. 
For the example box A10 in Figure 3.13, if the river exit cell is located in the 
southeast quadrant, then the three neighboring boxes for the southeast quadrant 
are Boxes A11, A20, and A21. The Mesh B Box B60, with dotted red lines, 
overlaps with four Mesh A boxes. The four sections of the Mesh B box are 
labeled here as a, b, c, and d which overlap with Boxes A10, A11, A20, and A21 
respectively. Since the Mesh A river exit cell is found in its southeast quadrant 
and is located in Box B60, then the position of the Box B60 river exit cell is 
important and will be examined. The Mesh B labels are shown exclusively for this 
explanation and are not used by the algorithm.  
 45 
 
Figure 3.13 Quadrant Labels for the Mesh B Box B60 
When the river exit cell for Box A10 falls into the southeast quadrant, the 
three downstream box possibilities are Boxes A11, A20, and A21. For the 
example in Figure 3.14, the river exit cell for Mesh B in POURPOINTS2 is 
located in quadrant d of the Box B60. Therefore, the downstream box for Box 
A10 is Box A21 and its flow direction is 2 according to the eight-direction 
pourpoint flow model. This scenario, Scenario One, is shown in Figure 3.14. 
 46 
 
Figure 3.14 Scenario One for the Flow Direction of Box A10 
There are two other options of flow direction for Box A10, which are 
Scenario Two and Scenario Three. The river exit cell of the Mesh B box could fall 
in quadrant c and then the downstream box would be Box A20 for Scenario Two. 
If the POURPOINTS2 cell were in quadrant b, then the example box would flow 
to Box A11 which is Scenario Three. The pictures for the two possibilities are 
shown below in Figures 3.15 and 3.16. 
 47 
 
Figure 3.15 Scenario Two for Flow Direction of Box A10 
 
Figure 3.16 Scenario Three for Flow Direction of Box A10 
The example with Box A10 shows the situation for boxes which fall 
completely within the border of the watershed or continent that is being upscaled. 
For these scenarios, the river exit cell of the Mesh B boxes was always located 
outside of the Mesh A box. In Section 3.3, the method is described for gathering 
 48 
the downstream information for the boxes which are within the watershed 
boundary in the vector format. Then, Section 3.4 addresses the inland catchment 
and continental margin situations, which are both sinks, when the river exit cells 
of Mesh B fall inside of the Mesh A box that it is exiting. 
3.4 DOWNSTREAM BOX INFORMATION FROM RASTER TO VECTOR FORMAT 
The downstream boxes have been identified by the upscaling procedure of 
the algorithm in fine resolution and in the grid format. The information must be 
translated to the coarse resolution in the vector domain. The raster to raster 
transfer of data is relatively simple with overlaid grids as illustrated in the 
previous section. The raster to vector formats are not quite as compatible and 
require more commands to share information. In this section, the steps for 
transferring the downstream box information from the fine resolution 
FLOWZONE0 grid to the original coarse mesh, PROJECTNET are described. 
An AML algorithm, pickgrid.aml (Hellweger, 1997), takes values from 
grids and places them in the corresponding location in the polygon attribute table 
of a coverage. For this algorithm, the item that links the downstream box 
information from the grid to the correct row of the polygon attribute table is the 
PROJECTNET identification number.  
First, the x and y coordinates of the centroids of each PROJECTNET box 
are added to the polygon attribute table. The x and y coordinates play a crucial 
role in linking the upstream and downstream boxes for the river network 
 49 
coverage. Then, a new field is created in the PROJECTNET polygon attribute 
table called Downstream. 
With the polygon attribute table prepared, Arcplot is executed which 
begins the ArcInfo graphical interface and query program. The coverage, 
PROJECTNET, is displayed in Arcplot. A cursor is declared in the coverage to 
enable the values from the FLOWZONE0 grid to be added into the Downstream 
column of the table. As a reminder, the FLOWZONE0 grid is a fine resolution 
representation of Mesh A. Each of the cells that make up the coarse box carries 
the value of the downstream box of the box that it represents. In other words, each 
cell in the raster form of the coarse mesh includes the PROJECTNET 
identification number of its downstream coarse mesh box. 
A DO loop is initiated which locates each coarse mesh box?s centroid and 
extracts the value of the FLOWZONE0 grid or the downstream box identification 
number. The number is placed in the Downstream column for the each coarse 
mesh box and the loop is continued until the cursor finishes with every centroid in 
the table. 
The attributes table of the coarse mesh at this point of the algorithm 
includes the standard ArcInfo columns including an identification number for 
each original coarse box, the x and y coordinates for the centroid of each box, and 
the identification number of its downstream coarse box. An example of part of an 
attributes table is shown here in Figure 3.17. 
 50 
 
Figure 3.17 Sample Portion of Coarse Mesh Attribute Table 
This transfer of the raster information to the vector format is the one of the 
steps in creating a complete coarse river network. The completed steps have 
addressed only the boxes which fall completely inside the continent or watershed. 
The next section will pay special attention to the boxes that intersect with the 
continental margin and which contain inland catchments. 
3.5 SINKS : CONTINENTAL MARGIN AND INLAND CATCHMENTS 
The goal of the algorithm in this section is to identify the x and y 
coordinates of the river exit cells that are sinks. Sinks can be located either along 
the continental margin or at an inland catchment. Sinks at the continental margin 
indicate the mouth of rivers. Inland catchments indicate a lake or depression for a 
watershed which does not drain to the ocean. Each continent has a few naturally 
occurring inland catchments, for instance the Great Salt Lake in the United States. 
The algorithm does not make a distinction between the two types of sinks. 
 51 
Sinks are distinguishable in the polygon attribute table since they are 
located within the boxes that have the same downstream box number as their box 
identification number. A few examples of this are seen in the Figure 3.17 from the 
previous section for PROJECTNET# 3, 5, 10 and 31 boxes. This effect of the box 
appearing to drain to itself happens for a logical reason and is explained here. The 
intersection of the coarse meshes and the flow direction grid in the first section 
results in irregularly shaped boxes along the continental border. The edge of the 
land surface essentially cuts off the original and secondary coarse meshes. 
Therefore, in a box along the continental border, the river exit cells for both 
meshes, the non-zero cells in POURPOINTS and POURPOINTS2, share the same 
location. An example is shown below in Figure 3.18 for the mouth of the Niger 
River in West Africa. The solid black lines represent the original coarse mesh 
boxes and the dashed gray lines are the secondary coarse mesh. The gray cell 
represents the river exit cells for both meshes. A similar situation occurs for the 
inland catchments except that their boxes are full-sized. 
 
 
 52 
 
Figure 3.18 Continental Border Box with the Same Location for the River Exit 
Cells of Both Meshes  
With the arcedit command initiated, the PROJECTNET polygon is chosen 
to be edited. The polygon boxes with the same downstream box as their own 
PROJECTNET# value are selected. A new coverage, EDGEPOLY, is formed 
with only the selected boxes, which are the boxes which appear to flow to 
themselves. The EDGEPOLY coverage, the boxes with sinks, is shown for Africa 
in Figure 3.19. 
 53 
 
Figure 3.19 Polygons from PROJECTNET that Exit to the Ocean or Inland 
Catchments 
Next, the grid mode is initiated to form a fine resolution grid from 
EDGEPOLY with the cells having the downstream box for their values. A mask is 
set with the new grid, EDGEGRID, which limits the analysis area for the 
following steps on the edge boxes and the inland catchments. With a conditional 
statement, a new grid, POURPTGRD, is created for the boxes which river exit 
cells for both meshes have the same location. The grid?s values are 
POURPOINTS2 values for every cell with a non-zero POURPOINTS value. 
 54 
The non-zero values cells are the sinks and a point coverage is created 
from the POURPTGRD grid called EDGEPOINTS. The x and y coordinates of 
the sinks are added to the EDGEPOINTS polygon attribute table because they 
need to be included in the river network. From the mouth of the Niger River 
example, Figure 3.20 shows that the EDGEPOINTS coverage has a point where 
the river exit cells are located.  
 
Figure 3.20 EDGEPOINT Coverage at the Mouth of the Niger River in West 
Africa 
An example of the point coverage of the river exit cells for Africa is given 
in Figure 3.21. 
 55 
 
Figure 3.21. Sinks for the Continent of Africa 
Since the transfer of information from grid to grid and from grid to 
polygon is complete, a few maintenance commands are performed here. Fine 
resolution grids can be extremely large and many of them are not needed after this 
section. Therefore, the unnecessary grids and coverages are deleted with a kill 
statement.  
 56 
3.6 COARSE RESOLUTION RIVER NETWORK 
The ultimate result of the DMA is the coarse resolution river network. The 
downstream box information is completely in the polygon format. The 
information needs to be consolidated and written to a line input file to create the 
river network. A few preparations of the data are required. 
First, the x and y coordinates of each original box, each downstream box, 
and each sink are joined into one polygon attribute table. The PROJECTNET 
table is joined with a copy of itself for the original box and downstream box 
coordinates. The sink coordinates are obtained from joining the EDGEPOINTS 
table with the PROJECTNET table. The names of the columns with the same 
titles are renamed so that they do not get overwritten.  
Now, the downstream and sink information is in the same attribute table. 
To create the river network or line coverage of the river network, the ArcInfo 
command generate is used. The format that the generate command uses is a 
number of a line segment, an x and y coordinate for the upstream node, an x and y 
coordinate for the downstream node, and the word ?end?. A sample for this type of 
file is shown here in Figure 3.22. 
 
 
 
 
 57 
7  
-2439332.25 , 
3868970.50 
-2469909.75 , 
3700791.25 
END 
8 
2330810.50 , 
3856037.00 
2574468.25 , 
3886034.00 
END 
9 
-2194514.00 , 
3840776.00 
-2469909.75 , 
3700791.25 
END 
Figure 3.22 Example of Input File for Generate/Line Command 
 58 
As previously stated, all of the coordinates are contained within the 
PROJECTNET attribute table and must be extracted and written to the text file to 
be used for the generate line command. A DO loop is initiated to extract the 
coordinate data. The boxes, which fall completely inside the continental border, 
have a different downstream cell value than their own identification number. 
Their x and y coordinates are taken accordingly for the upstream node, the center 
point of the original box, and the downstream node, the center point of the 
downstream box. 
For the edge boxes, their identification numbers match their downstream 
box numbers and can be distinguished by an if statement from the other types. For 
the boxes with the same downstream value as their value, the EDGEPOINTS x 
and y coordinates are used for the downstream node. 
The write statement makes the text file for the line coverage is part of the 
DO loop. When the algorithm has a successful run, it has created a river network 
file called RIVERS that links the centroids of the coarse mesh boxes. 
From the example of the mouth of the Niger River in Figures 3.18 and 
3.19, the river network result is shown here in Figure 3.23. 
 
 
 59 
 
Figure 3.23 River Network and Coarse Mesh for Mouth of Niger River 
 
 60 
RESULTS AND DISCUSSION 
Chapter 4 
In this chapter the results of the double maximum algorithm (DMA) are 
displayed and analyzed. The strengths and weaknesses of the algorithm are 
discussed. Comparisons are made between river networks extracted by the DMA 
and those resulting from two other upscaling methods. The contributions and 
limitations of the double maximum method are also discussed. 
4.1 DOUBLE MAXIMUM ALGORITHM APPLICATIONS 
The DMA produces a line coverage of the coarse scale river network for 
any continent or watershed for which the required input is provided. The user 
chooses the resolution of the river network. Initially, with the user?s input, a 
coarse resolution mesh is created which covers the continent or watershed. The 
links made between the centroids of the upstream and downstream boxes of the 
mesh form the coarse resolution river network. Each box has a single downstream 
box or one flow direction associated with it. The coarse resolution river network 
for Africa is shown in Figure 4.1 for the coarse mesh parameters provided in 
Appendix C. The figure is produced from a display in ArcView which is a user 
friendly way to view coverages and grids created in ArcInfo. The black boxes 
represent the coarse resolution mesh, and the line coverage of the river network is 
shown in blue. 
 61 
 
 
Figure 4.1 Coarse River Network and Coarse Mesh for the African Continent 
One advantage to the DMA is the incorporation of the mesh, which was 
created in geographic coordinates and translated to the projected environment for 
the execution of the program. With the river network as seen in Figure 4.1, the 
mesh can be projected back into geographic coordinates. Since the input 
parameters control the position of the mesh, the placement of the mesh can be 
 62 
created to correspond directly to the placement of the GCM boxes with the same 
number system. Therefore a transfer of the information of each box?s downstream 
box to a GCM database is easy. Also, the resolution of the GCM can also be 
correlated to match the coarse river network from this algorithm.   
 For clearer distinction of the rivers, an alternative method for dividing the 
land surface is accomplished with watershed boundaries. The same river network 
is shown in Figure 4.2 with the major watersheds of Africa. The outlines of the 
watersheds are shown in red, and the river network is shown in blue. 
 
 
 63 
 
Figure 4.2 Coarse River Network with Watershed Boundaries for the African 
Continent 
Viewing the results by continent, the river networks for the large 
watersheds are mostly located within the watershed boundaries even at this large 
scale of 2.8125? boxes or approximately 90,000-km2. This close representation is 
impressive considering the large scale of the mesh and that the naturally shaped 
watershed boundaries do not correspond to the mesh. The smaller watersheds that 
have an area less than one box or which are split by the arbitrarily placed mesh 
 64 
sometimes are represented as flowing into neighboring watersheds. These issues 
are discussed in Section 4.5. 
For a more detailed investigation of the algorithm?s results, a portion of 
West Africa?s watersheds are examined. The longest river network shown in 
Figure 4.3, which represents the Niger River, follows the overall direction of the 
river. The Niger?s headwaters fall on the Fouta Djalon region of Guinea in the 
southwestern part of the watershed. Flowing northeast into Mali, the river reaches 
Timbuktu as its northernmost point and turns south through the desert in Niger 
until it reaches the Atlantic Ocean in Nigeria. 
The connectivity of the river network is complete except for one box?s 
river segment near the mouth of the river. This separate segment represents a 
small river which is not part of the Niger River but part of its watershed. The river 
network is contained almost entirely inside of the watershed boundary with the 
exception of the narrow part of the watershed in the western region. The river 
networks for the smaller watersheds in the area fall less distinctly within their 
boundaries. A few of the smaller watersheds have joined together and share an 
outlet to the ocean. The Niger River and smaller watershed are shown in Figure 
4.3. with the same convention as the other figures with watershed boundaries 
shown in red lines and river networks shown in blue lines. 
 65 
 
Figure 4.3 Coarse Resolution Representation of Niger River with Watershed 
Boundaries 
In contrast to the more accurate Niger River network, the South American 
river networks are an example of a problem with the algorithm. Though the 
Amazon River flows within its borders, a neighboring watershed is included in 
the outflow. Because the mouth of the Tocantin/Araguaia river is located very 
close, within one coarse box length, to the mouths of the Amazon, the two river 
networks are joined. This amalgamation occurs since the maximum flow cell of 
the boxes in the outlet region has a higher value for the Amazon River than the 
smaller neighboring river. The Amazon River provides thirty percent of the 
world?s fresh water input from rivers to the oceans, and the input from the 
significantly sized river system, Tocantin/Araguaia, would increase this runoff 
 66 
value. The South American river networks are shown in Figure 4.4 with the same 
color convention as Figure 4.3. 
 
 
Figure 4.4 Amazon and Tocantin/Araguaia River Networks with Watershed 
Boundaries 
4.2 ANALYSIS OF DOUBLE MAXIMUM ALGORITHM 
In this section, the algorithm is examined in more detail. First, the 
versatility of the algorithm is described in Section 4.2.1. Then, the flow direction 
distribution is discussed in Section 4.2.2. 
 67 
4.2.1 Rotated Coarse Mesh 
Two of the strengths of the DMA are its ability to create river networks 
from a coarse mesh with any resolution and any orientation. The river networks 
and meshes shown previously all had the same 2.8125? resolution and the same 
north-south or perpendicular orientation as the grids. With the same resolution 
and grids at their north-south orientation, the algorithm was also executed with 
rotated meshes. The river network created from a mesh with a 45? rotation for 
Africa is seen in Figure 4.5. The variable orientation of the mesh is helpful since 
it is unique to this algorithm and it can be used to test or compare the algorithm?s 
results. From the Figure 4.6, the river network is displayed with the watershed 
boundaries and the accuracy of the placement of the rivers is acceptable. 
 
 68 
 
Figure 4.5 Coarse River Networks and Rotated Coarse Mesh for African 
Continent 
 69 
 
Figure 4.6 River Networks for Africa from Rotated Mesh shown with Watersheds 
The main similarity between the river networks created with perpendicular 
and rotated meshes is that the river network placement of the large watersheds is 
clear for both mesh orientations while the smaller basins become integrated into 
neighboring watersheds. Another similarity is the uneven flow direction 
distribution which is discussed in the next subsection. The closer view of part of 
West Africa in Figure 4.7 reveals a well-placed Niger River.  
 
 70 
 
Figure 4.7 Niger River Network with Watersheds 
4.2.2 Flow Direction Distribution 
The flow direction distribution of the coarse river network is uneven as 
there are more river segments exiting the boxes from the sides than from the 
corners. From the eight pour-point model, there are twice as many flow directions 
of 1, 4, 16, and 64 than flow directions of 2, 8, 32, and 128. This unbalanced 
distribution is logical considering the flow direction determination process for 
corner boxes. For every box, regardless of the quadrant where the river exit cell is 
located, there are two neighboring side boxes and one neighboring corner box as 
options for the downstream box. The two to one ratio is seen directly in the flow 
distribution. 
 71 
In this thesis, the flow segments that connect the boxes that share a side 
are called sides, and they correspond to the flow directions 1, 4, 16, and 64 from 
the eight direction pour-point model. The flow segments that direct water to one 
of the four boxes that touch the boxes at the corners are called corners and they 
correspond to the flow direction 2, 8, 32, and 128 from the eight pour-point 
model. A rotated box and its corresponding flow directions are seen in Figure 4.8. 
 
 
Figure 4.8 Eight Pour-point Model Illustration of Rotated Mesh Directions 
With this understanding of the side and corner directions, the values for 
the perpendicular and rotated river networks can be presented. For both the 
African and South American continents, the flow direction distributions are 
 72 
similarly skewed towards the side directions. Table 4.1 displays the flow direction 
distribution values for the two continents. 
Continent Orientation Percentage of Sides Percentage of Corners 
Africa Perpendicular 65.2 34.8 
Africa Rotated 45? 67.9 32.1 
South America Perpendicular 64.8 35.2 
South America Rotated 45? 62.2 37.8 
 
Table 4.1 Flow Direction Distributions for Two Continents 
The uneven flow direction distribution is present regardless of the mesh 
orientation. Other factors that seem not to influence the flow direction distribution 
are topography and mesh resolution. The continents of Africa and South America 
represent a great variation of land surface topography from the flat Pampas region 
of northern Argentina to the headwaters of the Congo River in the Ruwenzori 
Mountains in eastern Zaire. From a test of three main African watersheds with a 
0.5? mesh, the uneven flow distribution was also evident. 
4.3 EVALUATION AND COMPARISON TO OTHER RIVER NETWORKS  
This section examines the DMA?s results with other upscaling method 
results. A different upscaling algorithm called the flow generation algorithm 
(O?Donnell et al., 1999) is presented in Section 4.3.1. A ?manual? river network 
 73 
created from the visual inspection of the digital rivers was compared to the double 
maximum method in Section 4.3.2. Lastly, the observed river network from the 
Digital Chart of the World is observed with the double maximum river network.   
4.3.1 Flow Generation Algorithm 
The first river network to be compared with the DMA is the result of an 
upscaling algorithm developed by O?Donnell et. al. This ?flow generation? 
algorithm can be executed for only one watershed at a time with one input, a flow 
accumulation grid. Like the double maximum method, the algorithm can also be 
run with varying coarse resolutions for the output river network. 
The flow generation algorithm uses a scaling factor instead of a mesh and 
the scaling factor creates square or rectangular areas which are not projected. 
Therefore, the river network from the flow generation algorithm does not 
correspond to the same mesh as the DMA. The river networks can be created 
from roughly the same lower left hand corner and correspond well enough to be 
used in comparison. The river networks from the flow generation algorithm and 
the DMA are seen below for the Niger River in Figure 4.9. 
 
 74 
 
Figure 4.9 Niger River Network from the Flow Generation Algorithm (Left) and 
the DMA (Right) 
Though the same flow accumulation grid was used for each run, the river 
networks look different because of their different approaches. The river network 
created from the flow generation algorithm includes areas from outside of the 
river basin as delineated from the USGS processed digital elevation model. Since 
the algorithm only processes one watershed at a time, the regions with any flow 
accumulation cells with a non-zero value were integrated into the river network. 
The flow direction distribution is skewed towards the side directions more so than 
in the double maximum river network with 84 per cent of flow towards the sides 
and only 16 per cent of the flow to corner boxes. 
A comparison is seen in Figure 4.10 for the Congo River basin. Clearly, 
both rivers represent the water the flows in the basin well, but the DMA produces 
many more diagonal flow segments. 
 75 
 
Figure 4.10 Congo River Network from the Flow Generation Algorithm (Left) 
and the DMA (Right) 
4.3.2 Manual River Networks 
The next river network to view with the double maximum method is called 
the ?manual? river network because there is no program used to create the results. 
The river network is made from a visual inspection of the flow accumulation grid 
and the projected mesh. To determine the flow direction manually, the 
neighboring box whose river or tributary had the highest flow was examined. If 
the river meandered through a small portion of a box before flowing through the 
majority of the next neighboring box, then the second box in this description was 
chosen as the downstream box. The boxes along the continental margin which 
contain ocean outlets were not included in the manual river network.  
 76 
The manual river network is almost identical to the DMA river network. 
The network for the African continent is seen in Figure 4.11. Both the manual and 
the DMA river networks for the Niger River are shown in Figure 4.12. The 
manual segments, in green, that differ from the DMA network, in blue are 
displayed together.  
 
Figure 4.11 Coarse River Network from Visual Inspection of Flow Accumulation 
Grid for Africa 
 77 
 
Figure 4.12 Manual (Green) and Double Maximum (Blue) River Networks with 
the West African Watersheds 
 4.3.3 Observed Data River Networks 
The best way to compare the river network is with the real river or the best 
representation of the real river. The observed data from the Digital Chart of the 
World which is available for downloading from the website at 
http://www.maproom.psu.edu/dcw/. The river network is one of many themes that 
constitute the Digital Chart of the World. With the benefit of the fine resolution, 
the river cells appear more like a naturally meandering river than the straight lines 
from the algorithm. The river networks are shown together in Figure 4.13. For the 
 78 
Niger River especially, the placement of the DMA?s coarse river network to the 
observed data are very similar. 
 
 
Figure 4.13 Digital Chart of the World Fine River Network (Green) with DMA 
River Network (Blue) for Niger River Basin  
4.4 CONTRIBUTIONS 
The double maximum approach to resampling fine scale resolution grids 
to coarse resolution boxes produces the best representation of the flow of water 
over the land surface accomplished to this date. Compared to other existing 
techniques, the DMA makes three significant and innovative contributions to the 
modeling of land surface hydrology. The first contribution is the use of a 
 79 
projected coarse resolution mesh, and the second contribution is the ability to 
change the orientation of the mesh. The division of the coarse boxes into quarters 
to aid in determining the flow direction is the third contribution to acknowledge. 
This section describes the three contributions. 
4.4.1 Projection of Coarse Mesh 
Traditionally, upscaling algorithms have used the coarse resolution 
template of the general circulation models (GCMs). The GCM formats are either 
a mesh of square boxes or they are in geographic coordinates. Since geographic 
coordinates do not preserve land area, land surface hydrologists must work in a 
projected environment for more accurate predictions of flow length which greatly 
influence river routing. The main difference with the introduction of a projected 
mesh is that the ?curved? mesh lines do not correspond with the north-south 
orientation of the grid cells. As described in Section 3.3, some cells are located 
partly in two mesh boxes. For these cases, the cell is given the identification 
number of the box of which it is in the majority. This automatic decision making 
by ArcInfo works fine for the DMA and requires no adjustments to account for 
the use of non-perpendicular mesh. For the examples in this thesis, the mesh 
projections used were the same projections as the grids and were defined per 
continent. 
 80 
4.4.2 Orientation of Coarse Mesh 
The flexibility of the DMA to create meshes of varying orientation is the 
second main contribution. The use of the mesh instead of a scale factor allows for 
this control since the mesh properties required the angle of the mesh as input. The 
other variables of the mesh include the resolution, the shape (square or rectangle), 
and the placement of the mesh. Therefore, the adjustment of the orientation is yet 
another measure available for the user to exercise their mesh freedom. 
4.4.3 Division of Coarse Boxes 
The third contribution is its division of the coarse boxes into quarters. For 
methods which did divide upscaling areas, the coarse boxes have been divided 
into nine smaller and equally sized parts which correspond to the eight bordering 
boxes of the eight pour-point model. The DMA divides the coarse boxes into four 
equal sections with the same results as the nine-part division. The implications of 
this finding show that the division of the boxes from nine to four does not 
significantly affect the results. 
4.5 LIMITATIONS 
The two main limitations of the DMA have been mentioned in this 
chapter. The limitations are the flow direction bias and the small watershed 
integration to larger watersheds. This section includes possible solutions for the 
two issues. Since the suggested solutions may help either or both problems, they 
will be discussed simultaneously. 
 81 
4.5.1 Suggested Solution for the Integration of Smaller Watersheds  
One possible solution involves further tracking of the rivers from the 
boxes. In the current method, the river is followed outside of the boxes with the 
secondary mesh boxes. The ?smarter? tracking of the river could eliminate the 
integration of watersheds and would work as follows. 
The current method simply finds the maximum flow cells in each box of 
the original and secondary meshes. The secondary mesh maximum flow cell may 
be along a different river or tributary than the first maximum flow cell. Therefore 
the place where the majority of the water in the region of the box is taken into 
account but the river being tracked may be switched. For example, in one of the 
boxes in the Congo River basin, the tributary exits Box #2187 as seen in Figure 
4.14a and flows into the north neighboring bow before flowing into Box #2124. 
But the downstream box assigned to Box #2187 was Box #2189, the box directly 
west of the example box. The explanation for this ?wrong? direction is that the 
tributary that exited Box #2187 with the highest flow has a smaller maximum 
flow cell than the rivers in the secondary box for the region as seen in Figure 
4.14b. Therefore the flow direction could have been to the northeast while it 
actually changed to true west from the influence of the higher flow accumulation 
of the main channel.  
 82 
 
 
 
Figure 4.14 a) Fine River Network with Assigned Flow Direction in Blue b) Fine 
River Network with Maximum Flow Cells in Green for Tributary 
 83 
4.5.2 Suggested Solution for the Uneven Flow Direction Distribution 
The geometry of the eight bordering boxes for every box allows for the 
uneven distribution of the flow directions. The four side boxes have an automatic 
advantage to being chosen over a diagonal box. The reason is that for each box 
there are two chances for its secondary maximum flow cell to be placed in a side 
box and only one for it to be in the diagonal region. This leads to the idea of 
changing the shape of the mesh to find a more even flow distribution. The 
polygons of the mesh, which is overlaid on the watershed, could be a different 
shape.  
The octagon shaped could be created with a north-south and rotated mesh. 
Then the length of box for the maximum flow cell to fall would be equal as seen 
in Figure 4.15. Then the rotated mesh could be used for the secondary mesh and 
more diagonal directions would be obtained. 
  
 
Figure 4.15 Examples of Octagon Mesh Formations 
 84 
CONCLUSIONS 
Chapter 5 
The land surface component of the hydrologic cycle is an integral part of 
global-scale hydrological and climate models. With the advancement of satellite 
technology, the river networks that describe the land surface flow can be created 
for the world at increasingly finer resolutions, for example the GTOPO30 with 1-
kilometer grid cells. However, the global-scale climate models work with coarse 
resolutions, for example 2.8? boxes. Therefore, a methodology is needed to 
resample the fine resolution flow direction data into coarse resolution to be 
applied in climate models. In this thesis, an algorithm that was developed for 
resampling called the double maximum algorithm (DMA) is described and 
evaluated. The resulting coarse resolution river network, shown in blue, for a 
portion of West Africa is illustrated with the input fine resolution river network, 
shown in red, in Figure 5.1. 
 
 
 
 85 
 
Figure 5.1 Fine Resolution River Networks (Red) and Coarse River Networks 
(Blue) for West Africa 
Evolved from the resampling program by Olivera (1998), the DMA is 
written in Arc Macro Language for the GIS software, Arc Info, Version 7, and 
integrates the use of the coarse resolution mesh in its upscaling methodology. 
First, the fine resolution digital elevation model (DEM) is used to create flow 
direction and flow accumulation grids. Then the coarse resolution mesh, a 
polygon coverage, is overlaid onto the grids to divide the land surface into coarser 
boxes. Though the use of the mesh has advantages, the upscaling process is 
challenging because the flow direction information is translated between the grid 
and the coverage formats. By converting the coverages into grids, the algorithm?s 
translation process is achievable.  
 86 
The three contributions to upscaling that the algorithm introduces are 1) 
that the coarse resolution mesh can be projected, 2) that the orientation of the 
mesh can be changed and 3) that the mesh boxes are divided into four equal parts. 
The contributions are discussed further as their impacts show the strengths and 
limitations of the algorithm. 
The coarse resolution mesh is created in geographic coordinates and is 
projected into the same projection as the input grids. The importance of the 
projection is the connection that it makes between climate models and land 
surface hydrology. The climate models work with a mesh in geographic 
coordinates to communicate with the atmospheric component of the model. In 
contrast, the projected environment allows for the preservation of land area and is 
a necessary arena for land surface hydrologists. While the river network is created 
in a projected environment, it can be projected to geographic coordinates to be 
applied to climate models.  
The orientation of the mesh can be changed from the north-south 
orientation to any desired angle. Changing the orientation of the mesh has 
important implications in testing the algorithm?s flow direction distribution. The 
resulting river networks from using both the north-south oriented and the 45? 
rotated mesh show that the algorithm produces more flow directions from the side 
of the boxes than from the corners. Considering that the real river?s flow patterns 
should not alter with the arbitrary orientation of the mesh, the algorithm produces 
a biased distribution of flow directions. If the resulting river network depends on 
the orientation of the coarse resolution mesh, then the algorithm has a limitation.  
 87 
One method to decrease the uneven distribution of the flow directions 
from the sides of the boxes is changing the division of the mesh boxes. The 
division changed from nine to four equal parts through the development of the 
DMA. The quarterly division does affect the uneven distribution of flow 
directions by creating a river network with a better flow direction distribution. 
However, the uneven distribution continues to exist with the alternate division. 
Though the desired flow distribution is not necessarily known, the consistently 
higher number of flow directions to the sides shows biased results. With the 
DMA?s approach, the flow direction distribution is improved compared to the 
alternative upscaling methods.  
Future research in upscaling could include many different approaches. A 
potential approach to decrease the uneven flow distribution significantly would be 
to use different shapes for the division of the grids. For instance, the grids could 
be divided with octagons, and each edge of the octagon would be designated for 
one of the eight possible flow directions. Therefore, each side would have the 
same chance of hosting a river exit cell and could have a better distribution of 
flow directions. A different approach would be to view the watersheds by their 
natural boundaries instead of the arbitrary boxes of coarse resolution meshes.  
 
 
  
 88 
Appendix A 
Double Maximum Algorithm  
/* PROGRAM NAME: Double Maximum Algorithm 
/*  
/* PROGRAM FUNCTION: Create coarse scale river network in vector 
/* format from fine resolution flow direction and flow 
/*         accumulation grids in raster format.  
/*  
/* WRITTEN BY: Mary Lear, 
/*  Kwabena Asante, and Francisco Olivera 
/*  The algorithm includes an aml written by Ferdi Hellweger.  
/*  
/* WORKSHOP: Center for Research in Water Resources 
/* University of Texas 
/*  Austin, Texas 
/*  
/* DATE: March 22, 2000 - World Water Day 
/*  
/* INPUTS: 
/*  1) Fine Resolution Flow Direction Grid 
/*  2) Fine Resolution Flow Accumulation Grid, same resolution 
/*    as the Flow Direction Grid 
/*  3) Project File, *.prj 
/*  
/* NOTE: The commands in Section One are numbered for reference only. Read 
/*  the User?s Guide to Section One in Appendix B for more information. 
 
/* SECTION ONE: USER INPUT AND COARSE MESH GENERATION 
 
1) &sv fdr = [response 'Fine Resolution Flow Direction Grid: '] 
 
2) &sv fac = [response 'Fine Resolution Flow Accumulation Grid: ']  
 
3) &sv lon = [response 'Fishnet origin longitude: '] 
 
4) &sv lat = [response 'Fishnet origin latitude: '] 
 
5) &sv x = [response 'Y-Axis X-Coordinate: '] 
 89 
 
6) &sv y = [response 'Y-axis Y coordinate: '] 
 
7) &sv l = [response 'Cell Length: '] 
 
8) &sv h = [response 'Cell Height: '] 
 
9) &sv r = [response 'Number of Rows: '] 
 
10) &sv c = [response 'Number of Columns: '] 
 
11) &sv prj = [response 'Select projection file: '] 
 
12) generate geonet 
 
13) fishnet 
 
14) %lon%, %lat% 
 
15) %x%, %y% 
 
16) %l%, %h% 
 
17) %r%, %c% 
 
18) quit 
 
19) build geonet 
 
20) project cover geonet pronet %prj% 
 
21) clean pronet 
 
22) build pronet 
 
23) &sv long = %lon% - %l% * 0.5  
  
24) &sv lati = %lat% - %h% * 0.5 
 
25) &sv onemorerow = %r% + 1 
 
26) &sv onemorecol = %c% + 1 
 90 
 
27) generate geonet2 
 
28) fishnet 
 
29) %long%, %lati%  
 
30) %long%, %y% 
 
31) %l%, %h% 
 
32) %onemorerow%, %onemorecol% 
 
33) quit 
 
34) build geonet2 
 
35) project cover geonet2 pronet2 %prj% 
 
36) clean pronet2 
 
37) build pronet2 
 
 
/* SECTION TWO: UPSCALING PROCESS 
 
grid 
 
setwindow pronet %fdr%  
 
setcell %fdr% 
 
border = gridpoly ( con ( %fdr%, 1 ), 0.00000001 ) 
 
quit 
 
intersect border pronet projectnet poly 0.00001 nojoin 
 
intersect border pronet2 projectnet2 poly 0.00001 nojoin 
 
grid 
 
 91 
setwindow projectnet %fdr%  
 
setcell %fdr% 
 
projectgrid = polygrid(projectnet, projectnet#) 
 
maxfac = zonalmax(projectgrid, %fac%, DATA) 
 
pourpoints = con(maxfac == %fac%, %fdr%, 0) 
 
idgrid = polygrid(projectnet2, projectnet2#)   
 
maxfac2 = zonalmax(idgrid, %fac%, DATA) 
 
pourpoints2 = con(maxfac2 == %fac%, projectgrid, 0) 
  
quadrant = zonalmax(idgrid, pourpoints2, DATA)   
 
outgrid = con(pourpoints > 0, quadrant, 0) 
 
flowzone = zonalmax(projectgrid, outgrid) 
  
flowzone0 = con(isnull(flowzone), 0, flowzone) 
 
quit 
 
 
/* SECTION THREE: RASTER TO VECTOR FORMAT 
 
/* AML to pick a value from a grid and move to a polygon 
/* Written by Ferdi Hellweger and adapted by Kwabena Asante 
/*  and Mary Lear 
 
/* Replace projectnet with the name of your coverage 
/* Replace flowzone0 with the name of your grid 
 
/* Move polygon labels to centroid but ensure all labels within 
/* polygon 
 
centroidlabels projectnet inside 
 
/* Add X and Y coordinates to PAT and create field DOWNSTREAM 
 92 
 
addxy projectnet  
 
additem projectnet.pat projectnet.pat downstream 4 16 f 0 
 
/* Go into Arc Plot to read values from grid to polygon 
/* Display 1040 does not require a visual display, only an output file 
/* (distore) 
/* Useful for remote execution 
 
arcplot 
display 1040 
distore    
mape projectnet 
 
&s old$echo [show &echo] 
 
/*Start a loop to go through the PAT, find the cell value at each 
/*point location, and write it to the DOWNSTREAM item in the PAT. 
 
&type PICKVALUE: 
 
/* Declare and open a cursor to read and write to the PAT 
 
cursor cur1 declare projectnet.pat info rw 
cursor cur1 open 
 
&sv eof1 = .FALSE. 
&do &until %eof1% 
&sv x = %:cur1.x-coord% 
&sv y = %:cur1.y-coord% 
&sv downstream = [show cellvalue flowzone0 %x% %y%] 
&type PICKVALUE: %x% %y% %downstream% 
&s :cur1.downstream = %downstream% 
 
cursor cur1 next 
&if %:cur1.AML$NEXT% = .FALSE. &then 
        &sv eof1 = .TRUE. 
 
&end 
 
cursor cur1 remove 
 93 
 
&type PICKVALUE: 
&type PICKVALUE: Normal end. 
&type PICKVALUE: 
q 
 
/* SECTION FOUR: LINK TO SINKS - CONTINENTAL MARGIN and  
/*    INLAND CATCHMENTS 
 
/* Select only the polygons that discharge to sinks 
arcedit 
edit projectnet polygon 
select projectnet# = downstream 
put edgepoly 
quit 
 
build edgepoly 
 
/* Convert edge polygons to a grid and use as analysis mask 
grid   
setcell %fdr% 
setwindow %fdr% %fdr% 
edgegrid = polygrid ( edgepoly , downstream ) 
 
/* Set an analysis mask 
setmask edgegrid 
 
/* Find outlet cells within the analysis area 
pourptgrd = con ( pourpoints > 0, pourpoints2 ) 
 
/* Convert those to points, downstream includes just the nonzero 
/* cells! 
edgepoints = gridpoint ( pourptgrd, downstream ) 
 
quit 
 
addxy edgepoints point 
 
/* Perform maintenance 
 
kill border all 
 
 94 
kill pronet all 
 
kill pronet2 all 
 
kill projectgrid all 
 
kill maxfac all 
 
kill pourpoints all 
 
kill idgrid all 
  
kill maxfac2 all 
 
kill pourpoints2 all 
 
kill quadrant all 
 
kill outgrid all 
 
kill flowzone all 
 
kill flowzone0 all 
 
kill edgepoly all 
 
kill edgegrid all 
 
kill pourptgrd all 
 
 
/* SECTION FIVE: NEW COARSE RESOLUTION RIVER NETWORK 
 
copy projectnet second 
 
tables 
  
select second.pat 
alter x-coord dsx 12 f 3 c 
alter y-coord dsy 12 f 3 d 
q 
 
 95 
joinitem projectnet.pat second.pat projectnet.pat downstream downstream link 
 
/* Change column names in tables so they do not get overwritten  
 
tables 
 
select edgepoints.pat 
 
alter x-coord edgex 18 f 5 w 
alter y-coord edgey 18 f 5 e 
quit 
  
joinitem projectnet.pat edgepoints.pat projectnet.pat downstream 
 
cursor cur1 declare projectnet.pat info rw downstream > 0 and Area > 
15000000000 
cursor cur1 open 
 
cursor cur1 next  
&sv outfile = [open myfile.txt status -append] 
&sv eof1 = .FALSE. 
 
&do &until %eof1% 
 
&IF %:cur1.projectnet#% <> %:cur1.downstream% &THEN &DO 
 &sv upstx = %:cur1.x-coord% 
 &sv upsty = %:cur1.y-coord% 
 &sv downx = %:cur1.dsx% 
 &sv downy = %:cur1.dsy% 
         
 &sv m = %:cur1.projectnet#% 
 &sv a = [ write %outfile% %m% ]  
 
  &sv m = %upstx% , %upsty% 
 &sv a = [ write %outfile% [quote %m%] ]  
 
 &sv m = %downx% , %downy% 
 &sv a = [ write %outfile% [quote %m%] ]  
 
 &sv a = [ write %outfile% 'END' ]  
&end 
 
 96 
&IF %:cur1.projectnet#% = %:cur1.downstream% &THEN &DO 
 &sv upstx = %:cur1.x-coord% 
 &sv upsty = %:cur1.y-coord% 
 &sv downx = %:cur1.edgex% 
 &sv downy = %:cur1.edgey% 
  
 &sv m = %:cur1.projectnet#% 
 &sv b = [ write %outfile% %m% ]  
 
  &sv m = %upstx% , %upsty% 
 &sv b = [ write %outfile% [quote %m%] ]  
 
 &sv m = %downx% , %downy% 
 &sv b = [ write %outfile% [quote %m%] ]  
 
 &sv b = [ write %outfile% 'END' ] 
&end 
cursor cur1 next 
 
&if %:cur1.AML$NEXT% = .FALSE. &then 
 &sv eof1 = .TRUE. 
 
&end 
cursor cur1 remove 
 
generate rivers 
line 
&run myfile.txt 
end 
quit 
build rivers line 
 
 
FOR ROTATED MESHES: 
/* SECTION ONE: USER INPUT AND COARSE MESH GENERATION 
 
&sv fdr = [response 'Fine Resolution Flow Direction Grid: '] 
 
&sv fac = [response 'Fine Resolution Flow Accumulation Grid: ']  
 
&sv lon = [response 'Fishnet origin longitude: '] 
 
 97 
&sv lat = [response 'Fishnet origin latitude: '] 
 
&sv x = [response 'Y-Axis X-Coordinate: '] 
 
&sv y = [response 'Y-axis Y coordinate: '] 
 
&sv l = [response 'Cell Length: '] 
 
&sv h = [response 'Cell Height: '] 
 
&sv r = [response 'Number of Rows: '] 
 
&sv c = [response 'Number of Columns: '] 
 
&sv prj = [response 'Select projection file: '] 
 
generate geonet 
 
fishnet 
 
%lon%, %lat% 
 
%x%, %y% 
 
%l%, %h% 
 
%r%, %c% 
 
quit 
 
build geonet 
 
project cover geonet pronet %prj% 
 
clean pronet 
 
build pronet 
 
&sv rotatedlat = %lat% - 1.988738 
 
&sv onemorerow = %r% + 1 
 
 98 
&sv onemorecol = %c% + 1 
 
&sv rotatedy = %y% - 1.988738 
 
generate geonet2 
 
fishnet 
 
%lon%, %rotatedlat%  
 
%x%, %rotatedy% 
 
%l%, %h% 
 
%onemorerow%, %onemorecol% 
 
quit 
 
build geonet2 
 
project cover geonet2 pronet2 %prj% 
 
clean pronet2 
 
build pronet2 
 
 
 
 99 
Appendix B 
The User?s Guide to Section One 
Program Language: Arc Macro Language 
User Platform: ArcInfo, Version 7 or 8 
 
SECTION ONE: USER INPUT AND COARSE MESH GENERATION 
 
This section requires user input to customize the upscaling algorithm for the 
coarse resolution desired and the region for which the river network will be 
created. The algorithm creates a river network for one continent or watershed at a 
time.  
 
Lines 1-2: Input the flow direction and flow accumulation grids. 
 
The flow direction and flow accumulation can be of any resolution that is finer 
than the coarse resolution that is desired for the river network output. 
 
Lines 3-10: Input the parameters for the coarse resolution fishnet in geographic 
coordinates. 
 
The generate command for a fishnet requires a number of parameters to define 
the mesh. All of the inputs for the fishnet called GEONET are prompted with a 
brief description in ArcInfo while a more detailed explanation is provided here.  
 
?Fishnet Origin X-Coordinate (longitude)? is the X-Coordinate or the longitude of 
the lower left-hand corner of the fishnet. Two decimal places are recommended. 
 
?Fishnet Origin Y-Coordinate (latitude)? is the Y-Coordinate or the latitude of the 
lower left-hand corner of the fishnet. 
 
?Y-Axis X-Coordinate? orients the fishnet in space. For a perpendicular fishnet, 
the same value is used as for the Fishnet Origin X-Coordinate. 
 
?Y-Axis Y-Coordinate? orients the fishnet in space. For a perpendicular fishnet 
above the fishnet origin, a value of a few units greater than the Fishnet Origin Y-
Coordinate can be used.  
 
?Cell Length? refers to the length of the fishnet cells in decimal degrees. 
 100 
 
?Cell Height? refers to the height of the fishnet cells in decimal degrees. 
 
?Number of Rows? represents the number of rows in the fishnet. 
 
?Number of Columns? represents the number of columns in the fishnet. 
 
The suggested parameters for 2.8125? fishnets for each continent are provided in 
Appendix C. 
 
FOR ROTATED MESHES: The user must calculate a Y-Axis Y-Coordinate 
according to the rotation that the user wishes to introduce. 
 
Line 11: Input the projection file. 
 
Each projection and continent has different projection parameters. Use the same 
projection as the grids. Type the complete name of the projection file, i.e. 
lm_azafr.prj. Projection files are provided in Appendix D for the Lambert 
Azimuthal Equal Area projection for each continent. If you create a new prj file, 
write it in the correct format for the projection command. 
 
Line 12-19: Create the coarse resolution fishnet in geographic coordinates. 
 
The generate command executes the making of the fishnet. 
 
The fishnet, GEONET, is then ?built? to be given topology and be accessible to 
ArcInfo and ArcView.  
 
Lines 20-22: Project the coarse resolution fishnet. 
 
The fishnet, GEONET, is projected from geographic coordinates to a projected 
fishnet called PRONET using the .prj file named by the user.  
 
Lines 23-34: Create the second coarse resolution fishnet in geographic 
coordinates. 
 
The second fishnet, GEONET2, is an essential part of this program. GEONET2 is 
a fishnet of the same size and resolution as the original fishnet but its location is 
shifted. GEONET2 is offset from GEONET by half of the length and half of the 
height of the boxes. Figure B.1 below shows the first coarse resolution fishnet as 
solid black lines and the second fishnet is shown with dashed lines. 
 
 101 
  
Figure B.1. Origin Placement of the Original (Solid Black) and Second (Dashed 
Red) Fishnets 
The second fishnet is created from the input for the first fishnet with no additional 
input needed. The second fishnet origin is set to the southeast of the original 
fishnet with an offset distance of one-half of the box length and box height.   
 
To match the original mesh, the same length and height are used for the second 
fishnet. 
 
Since the second fishnet is offset from the original, the second fishnet requires 
one more row and one more column to extend over the edges of the original. 
 
The generate command executes the making of the fishnet. 
 
This fishnet, GEONET2, is also ?built? to be given topology and be accessible to 
ArcInfo and ArcView.  
 
FOR ROTATED MESHES: The equations for the ?Fishnet Origin Y-Coordinate 
(latitude)? and the ?Y-Axis Y-Coordinate? are changed for the second rotated 
mesh. The position of the second rotated mesh is below the original mesh as seen 
in Figure B.2. For this research with 2.8125? boxes, the second mesh origin is 
1.988378 units less than the user?s input for the original fishnet?s Y-Coordinate.  
Original fishnet 
origin (X,Y) 
Second fishnet 
origin 
(X-1/2L,Y-1/2H) 
 102 
The ?Fishnet Origin X-Coordinate? and the Y-Axis X-Coordinate? equations are 
unaffected. Section One of the algorithm for rotated meshes is seen at the end of 
Appendix A. 
 
  
Figure B.2 Origin Placement of the Rotated Original (Solid Black) and Second 
(Dashed Red) Fishnets 
 
Lines 35-37: Project the second coarse resolution fishnet. 
 
The fishnet, GEONET2, is projected from geographic coordinates to a projected 
fishnet called PRONET2 with the .prj file named by the user. 
 
Original rotated  
fishnet origin 
(X,Y) 
Second rotated 
fishnet origin 
(X,Y-1.99) 
 103 
Appendix C 
Guide to Coarse Resolution Mesh Parameters 
AFRICA 
Fishnet Origin Longitude: -20.00 
Fishnet Origin Latitude: -38.00 
Y-Axis X-Coordinate: -20.00 
Y-Axis Y-Coordinate: 32.00 
Cell Length: 2.8125 
Cell Height: 2.8125 
Number of Rows: 28  
Number of Columns: 29 
ASIA 
Fishnet Origin X-Coordinate (longitude): 36.00 
Fishnet Origin Y-Coordinate (latitude): -15.00 
Y-Axis X-Coordinate: 36.00 
Y-Axis Y-Coordinate: 32.00 
Cell Length: 2.8125 
Cell Height: 2.8125 
Number of Rows: 37  
Number of Columns: 67 
 104 
AUSTRALIA 
Fishnet Origin X-Coordinate (longitude): 95.00 
Fishnet Origin Y-Coordinate (latitude): -51.00 
Y-Axis X-Coordinate: 95.00 
Y-Axis Y-Coordinate: 32.00 
Cell Length: 2.8125 
Cell Height: 2.8125 
Number of Rows: 25  
Number of Columns: 32 
EUROPE 
Fishnet Origin X-Coordinate (longitude): -13.50 
Fishnet Origin Y-Coordinate (latitude): 9.00 
Y-Axis X-Coordinate: -13.50 
Y-Axis Y-Coordinate: 32.00 
Cell Length: 2.8125 
Cell Height: 2.8125 
Number of Rows: 26  
Number of Columns: 36 
NORTH AMERICA 
Fishnet Origin X-Coordinate (longitude): -180.00 
Fishnet Origin Y-Coordinate (latitude): 3.00 
Y-Axis X-Coordinate: -180.00 
Y-Axis Y-Coordinate: 32.00 
 105 
Cell Length: 2.8125 
Cell Height: 2.8125 
Number of Rows: 31 
Number of Columns: 55 
SOUTH AMERICA 
Fishnet Origin X-Coordinate (longitude): -95.00 
Fishnet Origin Y-Coordinate (latitude): -60.00 
Y-Axis X-Coordinate: -95.00 
Y-Axis Y-Coordinate: 32.00 
Cell Length: 2.8125 
Cell Height: 2.8125 
Number of Rows: 27 
Number of Columns: 23 
 
 106 
Appendix D 
Projection Files 
AFRICA 
INPUT 
PROJECTION GEOGRAPHIC 
UNITS DD 
PARAMETERS 
OUTPUT 
PROJECTION LAMBERT_AZIMUTH 
UNITS METERS 
PARAMETERS 
6378137.00000 
20 0 0 
5 0 0 
0.0 
0.0 
END 
ASIA 
INPUT 
PROJECTION GEOGRAPHIC 
UNITS DD 
PARAMETERS 
OUTPUT 
PROJECTION LAMBERT_AZIMUTH 
UNITS METERS 
PARAMETERS 
6378137.00000 
100 0 0 
45 0 0 
0.0 
0.0 
END 
AUSTRALIA 
INPUT 
 107 
PROJECTION GEOGRAPHIC 
UNITS DD 
PARAMETERS 
OUTPUT 
PROJECTION LAMBERT_AZIMUTH 
UNITS METERS 
PARAMETERS 
6378137.00000 
135 0 0 
-15 0 0 
0.0 
0.0 
END 
EUROPE 
INPUT 
PROJECTION GEOGRAPHIC 
UNITS DD 
PARAMETERS 
OUTPUT 
PROJECTION LAMBERT_AZIMUTH 
UNITS METERS 
PARAMETERS 
6378137.00000 
20 0 0 
55 0 0 
0.0 
0.0 
END 
NORTH AMERICA 
INPUT 
PROJECTION GEOGRAPHIC 
UNITS DD 
PARAMETERS 
OUTPUT 
PROJECTION LAMBERT_AZIMUTH 
UNITS METERS 
PARAMETERS 
6378137.00000 
-100 0 0 
 108 
45 0 0 
0.0 
0.0 
END 
SOUTH AMERICA 
INPUT 
PROJECTION GEOGRAPHIC 
UNITS DD 
PARAMETERS 
OUTPUT 
PROJECTION LAMBERT_AZIMUTH 
UNITS METERS 
PARAMETERS 
6378137.00000 
-60 0 0 
-15 0 0 
0.0 
0.0 
END 
 
 
 109 
References 
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http://www.ce.utexas.edu/stu/asanteko/home.html 
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Research. 22 (1986): 6S-14S. 
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Networks for Macro-scale Hydrology: Development and Analysis.? 
Manuscript in preparation. 
Hellweger, F. 1997. HEC-PREPRO: A GIS Preprocessor for Lumped Parameter 
Hydrologic Modeling Programs. Master?s Thesis, Department of Civil 
Engineering, University of Texas at Austin, Austin, Texas. 
Jenson, S.K. and J.O. Dominique. ?Extracting Topographic Structure from Digital 
Elevation Data for Geographic Information System Anaylsis.? 
Photogrammetric Engineering and Remote Sensing. 54 (1988): 1593-
1600. 
O?Donnell, G., B. Nijssen, D.P. Lettenmaier. ?Simple Algorithm for Generating 
Streamflow Networks for Grid-Based, Macroscale Hydrological Models.? 
Hydrological Processes. 13 (1999): 1269-1275. 
Olivera, F. ?Resampling a Flow Direction Grid ? AML Code.? (1998) 
http://www.ce.utexas.edu/prof/olivera/CoarseFDr/coarsefdr.htm 
Quinn, P., K. Beven, P. Chevalier, and O. Planchon. ?The Prediction of Hillslope 
Flow Paths for Distributed Hydrological Modelling Using Digital Terrain 
Models.? Hydrological Processes. 5 (1991): 59-79. 
Wolock, D.M. and C.V. Price. ?Effects of Digital Elevation Model Map Scale and 
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Resources Research. 30 (1994): 3041-3052. 
 
 110 
Vita 
Mary Stockley Lear was born on Tuesday, June 23, 1970. She completed 
her Bachelor of Science in Civil Engineering degree at the University of 
Washington in Seattle, Washington in 1993. Following college, she served as a 
water resources management engineer with the United States Peace Corps in 
Mali, West Africa for two years. Mary worked as a storm water management 
engineer at a consulting firm in downtown Seattle, Washington. In 1998, Mary 
returned to school at the University of Texas at Austin to study global hydrology 
and water resources engineering. 
 
Permanent address: 428 Herr Avenue 
Millersville, PA 17551 
 
This thesis was typed by the author.