DEVELOPMENT OF LARGE SCALE GRIDDED RIVER NETWORKS FROM VECTOR STREAM DATA 1

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1 JOURNAL OF THE AMERICAN WATER RESOURCES ASSOCIATION OCTOBER AMERICAN WATER RESOURCES ASSOCIATION 2003 DEVELOPMENT OF LARGE SCALE GRIDDED RIVER NETWORKS FROM VECTOR STREAM DATA 1 Francisco Olivera and Rajeev Raina 2 ABSTRACT: The Network Tracing Method (NTM) has been developed to determine gridded coarse river networks for modeling large hydrologic systems. For a coarse resolution grid, the NTM determines the downstream cell of each cell and the distance along the actual meandering flow paths between them. Unlike previously developed methods, the NTM uses fine resolution vector river networks as the source of information of the flow patterns rather than digital elevation models. The main advantage of using vector river networks as input is that they capture the hydrologic terrain features better than topographic data do, particularly in areas of low topographic relief. The NTM was applied to South America with a grid resolution of 1 degree by 1 degree and to the globe with a resolution of degrees by degrees. Overall, the method captured the flow patterns well. Generated digital river networks and drainage divides showed minor disagreement with those obtained from existing maps, and most of them were consistent with the resolution of the coarse river network. The majority of estimated basin areas were also close to documented values. River lengths calculated with the NTM, however, were consistently underpredicted. (KEY TERMS: river networks; surface water hydrology; global hydrologic modeling; continental hydrologic modeling; network tracing method.) Olivera, Francisco and Rajeev Raina, Development of Large Scale Gridded River Networks From Vector Stream Data. Journal of the American Water Resources Association (JAWRA) 39(5): INTRODUCTION Despite the widespread concern for the water problems of the world, no system is in place to produce a systematic, continuing, integrated, and comprehensive global picture of freshwater and its management (UNESCO, 2003). The development of large scale gridded river networks with resolutions compatible with the needs of global analysis is an essential part of the broader effort of modeling the water resources of the world. Many large scale river transport models are based on tracking water across the landscape through a network of interconnected cells (Vörösmarty et al., 1989; Liston et al., 1994; Miller et al., 1994; Sausen et al., 1994; Coe, 1997; Hagemann and Dümenil, 1998). To implement these models, the study area is subdivided into cells by overlaying a grid and the hydrodynamics within each cell is represented, for example, by a linear reservoir (i.e., a control volume in which the outflow is proportional to the volume stored). Individually, each cell constitutes the basic unit for which all energy and water balance calculations are performed, and collectively, the interconnected system of cells represents the flow patterns in the study area. Determining the interconnectivity between these cells is not a trivial task, especially when dealing with a large number of them. Determining this interconnectivity consists of identifying the downstream cell out of the eight neighbors of each grid cell. Thus, in gridded river networks, flow is allowed only along straight lines in the direction of the cell sides and corners from the center of a cell to the center of its downstream cell. Most available digital spatial datasets have a level of detail that supports hydrologic modeling of relatively small areas. Even datasets with global or national coverage are often clipped and used for modeling at a smaller scale. Some examples are the Digital Chart of the World (ESRI, 1993) and HYDRO1K (Gesch et al., 1999) for the world, and the National Hydrography Dataset (NHD) (USGS, 2003a), Hydrologic Unit Maps (USGS, 1987), and the National Elevation Dataset (NED) (USGS, 2003b) for the United States. In most cases, hydrologic modeling of large areas requires development of spatial data specifically oriented to that type of application. Coarse river 1Paper No of the Journal of the American Water Resources Association. Discussions are open until April 1, Respectively, Assistant Professor and Graduate Research Assistant, Texas A&M University, Department of Civil Engineering, 3136 TAMU, College Station, Texas ( /Olivera: folivera@civilmail.tamu.edu). JOURNAL OF THE AMERICAN WATER RESOURCES ASSOCIATION 1235 JAWRA

2 OLIVERA AND RAINA networks are an example of data developed with large-scale river transport modeling in mind. This paper advances the understanding of the global picture of freshwater by introducing a new method for developing coarse gridded river networks based on fine resolution stream network data in vector format. The method identifies the downstream cell of each cell of the system and estimates the flow distance between them. BACKGROUND In the past decade, efforts have been made to generate coarse river networks at global, continental, and large basin scales. Miller et al. (1994), for example, generated a 2 degree by 2.5 degree resolution global river network by manually determining the flow direction of each grid cell. Oki and Sud (1998) resampled a five-minute digital elevation model (DEM) to extract a one-degree global river network and calculated the ratio of the actual river lengths to the length according to their network, which on average was 1.4. With Oki and Sud s (1998) one-degree network as a base, Arora and Boer (1999) conducted another upscaling process to decrease the resolution to degree cells (i.e., 64 rows by 128 columns for the entire Earth) for use in global circulation models (GCMs). Similarly, Graham et al. (1999) resampled a 1 km DEM into five-minute, 0.5-degree, and onedegree DEMs, then burned in a fine resolution river network and created river networks from each of the resulting DEMs. Renssen and Knoop (2000) implemented the same approach as Graham et al. (1999) but used a five-minute DEM as input and generated a 0.5-degree global river network. Fekete et al. (2001) developed an upscaling method in which the flow direction of the cells is determined using the inverse of the maximum contributing area within the cell as the elevation value. Their method is illustrated by creating 10-, 15,- and 30-minute resolution river networks from a five-minute DEM for the Danube River basin in Europe. Likewise, O Donnell et al. (1999) proposed a method that, based on the contributing area, tracks the river network beyond the boundary of the grid cells. Olivera et al. (2002) generalized O Donnell et al. s (1999) approach by making it applicable to coarse resolution grids that are not aligned with the DEMs. With the exception of Miller et al. s (1994) global river network, all other methods use DEMs as the basic input. However, when it comes to evaluating the results, generated gridded networks are compared to fine resolution vector stream data. Thus, differences between the generated gridded networks and the fine resolution vector stream data can be largely explained by inconsistencies between the DEM (used for generating the gridded network) and the fine resolution stream data (used for evaluating the results). That is, the streams delineated from the DEM do not coincide with the fine resolution stream data. From this point of view, Graham et al. s (1999) and Renssen and Knoop s (2000) networks have a higher chance of matching fine resolution river networks because of the burning in stream process they included, which consists of modifying the DEM by imposing the stream data on it. In general, vector fine resolution stream data appear to be the natural input for determining coarse river networks because they capture the hydrologic terrain features better than DEMs do, particularly in areas of low relief where minor inaccuracies in the topographic data may lead to major errors in the delineation of streams. Additionally, vector fine resolution stream lines are easier to trace downstream after they leave the cell for which the flow direction is being determined. Therefore, the use of vector stream data for generating gridded river networks is an alternative worth exploring. Likewise, because of the law of large numbers (DeGroot, 1986), it can theoretically be assumed that over large areas the likelihood of water flowing in any direction is the same. Accordingly, it can be considered that in gridded river networks the likelihood of flow in any of the eight possible directions should be the same. Flow direction distributions in which all directions have the same likelihood of occurrence are called here balanced distributions. For the case of gridded river networks with unbalanced flow direction distributions, Olivera et al. (2002) discuss the sensitivity of their flow patterns to the grid orientation. After generating gridded river networks for Africa and South America, they rotated the grids 45 degrees (i.e., switching side and corner directions) and generated new networks of the two continents for the rotated grids. The networks of both continents generated for the two grid orientations were then compared. After this comparison, they concluded that when the flow direction distributions are not balanced, the flow patterns are affected by the grid orientation in addition to the terrain topography. Olivera et al. (2002) made a study of the bias some upscaling river network methods have toward predicting more flow through the sides than through the corners of the cells. According to them, this bias is caused by the fact that most of these methods treat cell sides and corners differently. Note that preference for flow in a specific direction can occur in actual basins, but these preferences should be included in the analysis through the fine resolution stream data JAWRA 1236 JOURNAL OF THE AMERICAN WATER RESOURCES ASSOCIATION

3 DEVELOPMENT OF LARGE SCALE GRIDDED RIVER NETWORKS FROM VECTOR STREAM DATA used as input and not by a bias in the upscaling method. Olivera et al. (2002) also showed that for a grid with identical square cells, a balanced flow direction distribution produces equal flow lengths over the orthogonal and diagonal directions and has a side to corner ratio of 59:41 (i.e., 59 percent of the cells flow out through the sides and 41 percent through the corners). They found that previously developed coarse networks, as well as the networks developed with their method, had side to corner ratios greater than 59:41. River networks developed by O Donnell et al. (1999), Arora and Boer (1999), and Olivera et al. (2002) had side to corner ratios for the Congo River basin of 74:26, 79:21, and 62:38, respectively, and for the Niger River basin of 72:28, 70:30, and 62:38, respectively. Additionally, Olivera et al. s (2002) global network had a ratio of 68:32. Therefore, it appears necessary to develop a new algorithm that ensures balanced flow direction distributions. Finally, because of their coarse resolution, gridded river networks cannot capture the longer flow lengths of meandering rivers. By representing the streams with straight lines that connect the center of the cells, gridded networks overlook the complexity of the flow patterns and underestimate the river lengths. Accurate flow distance estimation is necessary for tracking the motion of water on the landscape and for calculating travel times from one point to another. Because the method presented here is based on fine resolution stream data, the actual stream lengths are already known and can be used for improving the calculation of the gridded river lengths. Therefore, it seems necessary and promising to develop a method that, while generating coarse resolution river networks, captures the flow distance information available in fine resolution stream data. This algorithm will assign a meandering factor to each line of the gridded network. The meandering factor is defined as the flow distance from a cell to its downstream cell along the fine resolution flow path divided by the flow distance along the coarse resolution flow path (i.e., the length of the cell side or cell diagonal, depending on the flow direction in the cell). Improving with respect to previous upscaling river network methods, this paper: (1) explores the use of vector fine resolution stream data for generating coarse gridded river networks, (2) presents an algorithm for developing gridded river networks with balanced flow direction distributions, and (3) presents an algorithm for incorporating fine resolution flow distance information into coarse resolution networks. This paper builds on previous work by the first author (Olivera et al., 2002) and was motivated by the need to address some limitations of previous methods that use DEMs as the source of the flow patterns. METHODOLOGY The method presented in this paper is called Network Tracing Method (NTM) because of its capability to trace flow paths downstream over the river network. This section covers the principles of the method as well as the interpretation of the resulting gridded river networks. NTM Principles Given a coarse resolution grid that subdivides a study area into identical square cells and a fine resolution dendritic river network of the same area, the NTM identifies the downstream cell of each grid cell of the system in which a stream is found and estimates meandering factors for the predicted streams. Gridded river networks generated by the NTM have balanced flow direction distributions. Defining grids in geographic coordinates (i.e., longitude and latitude) is common practice in global hydrologic modeling. Grid cells defined in geographic coordinates, however, get distorted when projecting the curved surface of the earth onto the flat surface of a map. A degree by degree cell in geographic coordinates, for example, will not be square and will not be necessarily identical to other degree by degree cells after projecting it to the map, especially if it is located close to the poles (see Figure 1). The NTM allows the use of distorted cells; however, the algorithm for estimating whether the flow direction distribution is balanced assumes identical square cells. The less the cells resemble identical squares, the less accurate this estimation will be. Likewise, grid cells in which streams are not found represent dry areas for which determining a flow direction would not be necessary. Thus, with respect to the DEM based methods, the NTM has the advantage that it defines flow patterns only where the hydrography indicates the existence of watercourses. However, not finding a stream in a cell can also respond to inconsistency between the resolution of the coarse grid and the density of the stream data (i.e., a grid resolution finer than what the river network supports). Finding cells with no streams in areas not known as dry indicates that the grid cell size is too small for the river network. Figure 2a presents a detail of a coarse resolution grid (i.e., a nine-cell window) and of its corresponding fine resolution dendritic river network. In the network, the lines need to connect to each other only at their edges or end points, also called nodes, and point downstream. Because of the dendritic character of the network, a line can have more than one line JOURNAL OF THE AMERICAN WATER RESOURCES ASSOCIATION 1237 JAWRA

4 OLIVERA AND RAINA upstream, but only one line downstream. For the same reason, a node can be the downstream node of more than one line but can be the upstream node of one line only. Intersection of the fine resolution river network with the coarse resolution grid results in a new network in which the lines are split at the grid cell boundaries, so that each line lies entirely within one cell (see Figure 2b). In the intersection process, the cell number in which each line is located and its length are stored in the fine resolution network table (see fields Grid Cell and Length in Table 1). Additionally, each end point of the network lines is randomly assigned a unique number (see Figure 2c), and these are stored in the network table as the upstream and downstream nodes (see fields Upstream Node and Downstream Node in Table 1). Moreover, the upstream flow length of a node is calculated as the greatest of the distances from the node itself to each of the nodes located upstream. Likewise, the upstream flow length of a line is calculated as the upstream flow length of its downstream node. The upstream flow length of a line is stored in the network table (see field Upstream Length in Table 1). Figure 1. Coarse Resolution Grid Cells in the Area of Alaska (North America) After Projecting Them Into Lambert Azimuthal Projection. Note that the sides along the north-south direction are significantly longer than the sides along the west-east direction. The next step of the NTM consists of identifying the exit node of each grid cell. Exit nodes are the points through which the main streams leave the cells. With the exception of the continental margin and of closed depressions, exit nodes are located at the boundary of the cells. Cells at the continental margin and closed depressions are sink cells and do not have exit nodes. The exit node of a cell is defined as the node with the greatest upstream flow length. However, rather than defining the exit node based on the greatest upstream flow length, the modeler can consider other criteria like the greatest flow or drainage area. In this study, the upstream flow length was preferred because it can be calculated from the fine resolution river network dataset already in use. Once the exit nodes of the cells have been located, their numbers are stored in the coarse-resolution grid table (see field Exit Node in Table 2). The network is then traced downstream to identify the next exit nodes, which are the exiting nodes for the cells located immediately downstream. Note that the next exit nodes do not necessarily have the greatest upstream flow length among the nodes of the cell. They are found simply by tracing downstream from the corresponding cell exit node. The numbers of the next exit nodes are stored in the grid table (see field Next Exit Node in Table 2). The flow distance between the exit node and the next exit node of each cell, called here reach length, is then calculated and stored in the grid table (see field Reach Length in Table 2). Note that sink cells do not have reach lengths. The reach length is subsequently compared with a user defined threshold distance. A reach length greater than the threshold implies the cell is flowing to its immediate downstream cell, while a reach length less than the threshold implies that it is flowing one cell farther downstream. This comparison is shown in the grid table (see field Comparison with Threshold in Table 2). The rationale of the method indicates that if a stream enters a cell and stays in it for a distance greater than the threshold, then that cell can be considered the downstream cell; otherwise, it is considered that the stream does not stay long enough in the cell and that it just uses the cell as a stepping stone on its way to the one cell farther downstream. In the latter case, after additional network tracing, the next exit node has to be replaced with the next in sequence exiting node and the reach length recalculated. These new next exit node number and reach length are stored in the grid table [see fields Next Exit Node (Corrected) and Reach Length (Corrected) in Table 2]. This feature of the method has been included to allow the user to adjust the number of cells flowing through the sides and through the corners until a balanced flow direction distribution is obtained. JAWRA 1238 JOURNAL OF THE AMERICAN WATER RESOURCES ASSOCIATION

5 DEVELOPMENT OF LARGE SCALE GRIDDED RIVER NETWORKS FROM VECTOR STREAM DATA Figure 2. Detail of the Study Area (i.e., nine-cell window): (a) Coarse Resolution Grid With Cell Labels and Original Fine Resolution Vector River Network; (b) Fine Resolution River Network, After Intersection With Grid, With Segment Labels; (c) Fine Resolution River Network With Node Labels; and (d) Coarse Resolution River Network. Balanced flow direction distributions can be obtained by changing the threshold value until the side to corner ratio equals 59:41 (Olivera et al., 2002). Note that as the threshold value increases, so does the number of cells flowing through the corners causing the side to corner ratio to decrease and vice versa. In an extreme case, when using a very small threshold value, no flow through the corners would be predicted. When using a very large threshold value, the maximum possible number of cells with flow through the corners would be predicted. Ideally, the threshold should be set such that the eight flow directions are equally likely to occur. Threshold values depend on the grid cell size and on the level of detail of the fineresolution stream data. Finally, the downstream cell is defined as the cell that drains through the next exit node, and its number is stored in the grid table (see field Downstream Cell in Table 2). Once the downstream cells are identified, a gridded river network can be obtained (see Figure 2d). Likewise, the grid cells are assigned a flow direction code and a meandering factor, which are stored in the grid table (see fields Flow Direction Code and Meandering Factor in Table 2). The flow direction code is a number associated with the direction in which the flow takes place. ESRI (1992), for example, uses a code in which 1 corresponds to the east direction, 2 to the southeast direction, 4 to the south direction, and 8, 16, 32, 64, and 128 are defined accordingly, assuming north points upward. Likewise, if the flow is through the cell side, the meandering factor is equal to the reach length divided by the grid cell size. If the flow is through the corners, the meandering factor is equal to the reach JOURNAL OF THE AMERICAN WATER RESOURCES ASSOCIATION 1239 JAWRA

6 OLIVERA AND RAINA length divided by 1.41 times the grid cell size. In most cases, this factor is greater than one because the presence of meanders is not captured by the coarse resolution river network. However, factors lower than one can also be found and are associated with the relative location of the exit nodes of consecutive cells. Note that by definition, sink cells are assigned downstream cell, flow direction code, and meandering factor values equal to zero. TABLE 1. Fine Resolution Network Lines. Grid Upstream Downstream Upstream Line Cell Length* Node Node Length* A B C D E F G H I J K L M N O *In the same units of length as the fine-resolution stream data. Two exceptions to the method are worth mentioning. The first exception consists of cells whose downstream cell is not one of their eight neighbor cells. This situation occurs when the threshold value is greater than the cell size, and the river network crosses the cell s downstream cell from side to opposite side along a flow path that is shorter than the threshold (see Figure 3a). According to the method, the downstream cell would be two cells down, in the direction of one of the sides. This case has been corrected by redefining the downstream cell as the immediate downstream cell without further tracing of the network, even though the reach length would be less than the threshold. The second exception consists of pairs of adjacent cells pointing to their downstream cells along diagonals that intersect each other. This situation can be found, for example, when a stream flows around the corner of four cells (see Figure 3b). This case has also been corrected by redefining the downstream cells as the immediate downstream cells, even though the reach lengths would be less than the threshold. Note that the immediate downstream cells are always in the direction of the sides and that no intersection can occur when cells point to their downstream cells along their sides. Interpreting Coarse Gridded River Networks After developing coarse gridded river networks, major basins and rivers can be identified, and their areas and lengths can be calculated. Basin areas determined from coarse river networks tend to be overestimated in the case of large basins and underestimated in the case of small basins. The TABLE 2. Coarse Resolution Grid Cells. Next Comparison Next Exit Reach Flow Exit Exit Reach With Node Length* Downstream Direction Meandering Cell Node Node Length* Threshold (corrected) (corrected) Cell Code Factor Less Than Greater Than Less Than Greater Than Less Than Greater Than Greater Than Greater Than *In the same units of length as the fine resolution river network and coarse-resolution grid. Note: Threshold equal to 70 units of length. JAWRA 1240 JOURNAL OF THE AMERICAN WATER RESOURCES ASSOCIATION

7 DEVELOPMENT OF LARGE SCALE GRIDDED RIVER NETWORKS FROM VECTOR STREAM DATA Figure 3. Exceptions to the Basic Rules of the NTM. (a) Because the length from Node 133 to Node 139 is less than the threshold value, the algorithm assigns Cell 57 as the downstream cell of Cell 97, when the correct one is Cell 77; and (b) because of their short reach length, Cells 77 and 78 are assigned downstream Cells 58 and 57, respectively, defining intersecting flow paths, when the correct ones are 78 and 58. reason for this overestimation and underestimation is that when generating coarse river networks a single downstream cell is assigned to each cell, regardless of the different directions in which each of the fine resolution streams flow out of the cell (see Figure 4). That is, whenever two or more fine resolution streams coincide in a grid cell, the smaller streams and their corresponding drainage areas become absorbed by the cell s main stream. This process tends to make larger basins larger and smaller basins smaller. This problem, though, is intrinsic to the upscaling process itself and is not caused by the NTM. Additionally, basin areas are overestimated because sink cells are counted as part of the basins, even though they are only partially within it. The relevance of this error increases with the grid cell size. It can be proved that, on average, basin areas are overestimated by half a cell because of the sink cells. Likewise, river lengths tend to be underestimated for two reasons. First, this occurs because of how meandering factors are calculated at the river mouths. By definition, the meandering factors of the sink cells are equal to zero. Similarly, the meandering factors of the cells located immediately upstream of the sink cells are equal to the length of the stream segment in the sink cell divided by the cell size. It can be proved that, on average, the river length is underestimated by one cell size at the river mouths (see Figure 5). Second, the underestimates occur because the NTM has problems calculating reach lengths and meandering factors when a stream crosses back and forth from one cell to its adjacent cell (see Figure 6). Under these circumstances, the reach length and meandering factors are underestimated because the method traces the network only in the immediate two downstream cells. The reach length is calculated as the flow distance between the exit node and the next exit node of a cell; however, since the stream could be entering and leaving the downstream cell a number of times, the next exit node does not really represent the point at which the stream definitely leaves it. Although this situation affects a limited number of cells, it can cause significant underestimation of overall river lengths. APPLICATION, RESULTS, AND DISCUSSION The NTM was applied to South America with a resolution of 1 degree and to the globe with a resolution of degrees. The HYDRO1K vector stream JOURNAL OF THE AMERICAN WATER RESOURCES ASSOCIATION 1241 JAWRA

8 OLIVERA AND RAINA network (Gesch et al., 1999) was used as the fine resolution stream data. Cell Size = L Actual Length = P+ Q+ R+ S Predicted Length = L S + L[ 0] L = S Figure 4. The Mekong, Salween, and Yangtze Rivers in Southern China. Note that the cell with thick outline flows to the east following the Yangtze River, the largest of the three, although the other two rivers flow south. Figure 5. At the River Mouth, the Meandering Factors Are Zero for the Sink Cell (by definition) and S/L for the Immediate Upstream Cell, Causing an Error in the Estimated River Length in the Two Cells of P+Q+R, Which is in the Order of Magnitude of L. HYDRO1K is a set of global hydrologic raster and vector datasets developed by the USGS Earth Resources Observation Systems (EROS) Data Center. The HYDRO1K dataset consists of a global DEM with resolution of 1 km and its derivatives, which include watershed boundaries and stream networks in vector format. The HYDRO1K vector stream network was used here because it is currently the only vector global network that: (1) has a dendritic shape, (2) correctly connects the lines at their edges without gaps or overlapping segments, and (3) has its lines pointing downstream three conditions necessary to apply the NTM. The conditions the NTM imposes on the network, though, are standard in network analysis and are not unique to this method. The method was evaluated based on two criteria: (1) comparison of shapes and areas of delineated and actual basins and (2) comparison of shapes and lengths of delineated and actual streams. Delineated basin areas were compared with those documented by Revenga et al. (1998), and delineated river lengths were compared with those of the fine resolution river network provided by the HYDRO1K dataset. South America The NTM was applied first to South America using a coarse grid with resolution of 1 degree by 1 degree. The grid was defined from 82 W, 56 S to 34 W, 13 N and had 3,312 cells arranged in 69 rows and 48 columns. It was subsequently projected using a Lambert Azimuthal Equal Area map projection with origin at 60 W, 15 S. The average side and area of the resulting cells were km and 10,821 km 2, respectively. The NTM was then applied with different threshold values until the side to corner ratio was 59:41, which corresponds to a balanced flow direction distribution. For this side to corner ratio, the threshold was km, 833 cells flowed through their sides, 592 through their corners, 187 were sinks at the continental margin or closed depressions, and 1,700 did not contain stream segments (i.e., cells located in the ocean). Additionally, no cells without stream segments were found within the continent boundaries, indicating compatibility of the grid resolution with the fine resolution river network. JAWRA 1242 JOURNAL OF THE AMERICAN WATER RESOURCES ASSOCIATION

9 DEVELOPMENT OF LARGE SCALE GRIDDED RIVER NETWORKS FROM VECTOR STREAM DATA were not used and 4,332 km and 3,448 km when the meandering factors were used. The corresponding lengths according to HYDRO1K were 4,766 km and 3,573 km. The use of the meandering factors improved the estimation of the river lengths, although errors of 9.1 percent and 3.5 percent were still made because of the problems associated with the calculation of meandering factors discussed in the previous section. Cell Size = L P+ Q+ R+ S+ T Actual Meandering Factor = 2 L P+ Q Predicted Meandering Factor = 2 L Figure 6. When a Stream Crosses Back and Forth From One Cell to Its Adjacent Cell, the Meandering Factor is Calculated as P+Q/ 2 L Rather Than as P+Q+R+S+T/ 2 L, Causing an Error in the Estimated River Length of R+S+T. Figure 7 shows the coarse river network and drainage divides of the basins larger than 500,000 km 2 of South America determined with the NTM. For comparison purposes, Figure 8 shows the streams and drainage divide according to the NTM and HYDRO1K for the Orinoco River basin, located in northern South America. In Figure 8, for the Orinoco River basin, it can be seen that the drainage divide and streams according to both datasets correspond well, given the unavoidable limitations of a dataset based on a grid with a resolution coarser than 100 km. Comparison of the basin areas according to the NTM and Revenga et al. (1998) is presented in Table 3. Note that errors in the drainage areas were below 10 percent in nine out of 10 cases and below 5 percent in seven out of ten cases and that no striking errors were found. Furthermore, the river lengths of the Amazon and Parana Rivers according to the NTM were 4,269 km and 3,123 km, respectively, when the meandering factors Globe Figure 7. Coarse Resolution River Network and Drainage Divides of South America According to the NTM (based on a 1 by 1 grid). Only basins larger than 500,000 km 2 were considered in the figure. The NTM was then applied to the entire globe using a coarse grid with a resolution of degrees by degrees. Since HYDRO1K data were not available for Australia, only Africa, Asia, Europe, North America, and South America were considered in the analysis. Table 4 shows parameters of the map projections and coarse grids used for each of the five continents. Table 5 shows properties of the five river JOURNAL OF THE AMERICAN WATER RESOURCES ASSOCIATION 1243 JAWRA

10 OLIVERA AND RAINA Figure 8. River Networks and Drainage Divides of the Orinoco River Basin in South America According to HYDRO1K and the NTM (based on a 1 by 1 grid). TABLE 3. Area of South American Basins (km 2 ). Revenga et al. Error Basin (1998) NTM (percent) Amazon 6,144,727 5,935, Parana 2,582,672 2,814, Madeira (Amazon) 1,485,218 1,428, Paraguay (Parana) 1,168,540 1,314, Orinoco 953, , Tocantins 764, , Marañon-Ucayali (Amazon) 735, , Rio Negro (Amazon) 720, , Sao Francisco 617, , Xingo (Amazon) 520, , Note: Only basins larger than 500,000 km 2 have been included. NTM refers to estimated values with a grid resolution of 1 by 1. networks obtained with the NTM for each continent. For Africa and South America, the threshold distance was modified until the side to corner ratio was equal to 59:41. This was not possible, though, in the case of Asia, Europe, and North America because of the presence of land close to the North Pole. At these high latitudes, because of the distortion caused by the projection of the grid, some grid cells had two sides significantly longer than the other two, as shown in Figure 1. This distorted grid geometry caused the NTM to give preference to flow through the longer sides. For these three continents, the minimum JAWRA 1244 JOURNAL OF THE AMERICAN WATER RESOURCES ASSOCIATION

11 DEVELOPMENT OF LARGE SCALE GRIDDED RIVER NETWORKS FROM VECTOR STREAM DATA TABLE 4. Map Projection and Coarse Resolution Grid Parameters and Properties. Africa Asia Europe North America South America Map Projection Lambert Lambert Lambert Lambert Lambert Map Projection Origin (20, 5 ) (100, 45 ) (20, 55 ) (-100, 45 ) (-60, -15 ) Southwestern Corner (-22.5, ) ( , 0 ) ( , ) (-180, ) ( , ) Northeastern Corner ( , ) (180, ) ( , ) ( , ) (-33.75, ) Number of Cells 783 1, , Number of Rows Number of Columns Average Cell Side (km) Average Cell Area (km 2 ) 89,712 66,073 63,265 63,820 85,616 Note: Lambert map projection refers to Lambert Azimuthal Equal Area. Negative coordinate values refer to West longitudes and South latitudes. TABLE 5. River Network Properties. Africa Asia Europe North America South America Threshold (km) Side to Corner Ratio 59:41 67:33 69:31 67:33 59:41 Cells Flowing Through Their Sides Cells Flowing Through Their Corners Sink Cells Cells in the Ocean achievable side to corner ratio, which was greater than 59:41, was used (see row Side to Corner Ratio in Table 5). Figure 9 shows the river network for the entire world obtained with the NTM, in which the main river systems can be recognized. For the world basins greater than one million km 2, Table 6 presents a comparison of the basin areas according to Revenga et al. (1998) and those determined with the NTM. Note that in this case, errors were below 10 percent in 18 out of 23 cases and below 5 percent in 9 out of 23 cases. As expected, percentage errors in basin areas increased with respect to the case presented in the section titled South America, given that the grid resolution increased from 1 degree to degrees. For the world rivers longer than 4,000 km, Table 7 presents river lengths reported by the HYDRO1K and NTM. NTM river lengths were calculated with and without using meandering factors. It can be noted that although river lengths calculated using meandering factors have large errors, these errors are overall less than those made when no meandering factors were considered. In Table 6, note that all errors greater than 10 percent are positive, which is consistent with the fact that large basins tend to absorb smaller drainage areas and become even larger. An interesting case of this situation is found in southern China, where at a certain location the Mekong, Salween, and Yangtze Rivers are less than 75 km apart (see Figure 4). At this location, the three rivers share the same grid cell, and even though the actual rivers do not flow downstream in the same direction, the gridded network identifies only one downstream cell. In this case, the largest river (the Yangtze) absorbed the upstream drainage area of the other two. This situation explains the positive error of 30 percent in the area of the Yangtze River basin as well as the short length estimated for the Mekong River. For the specific case of the African continent and the Congo River and Niger River basins, comparison of the NTM with previously developed methods shows that for predicting basin areas the NTM does better than Olivera et al. (2002), but not as well as Arora and Boer (1999) (see Table 8). However, for generating balanced river networks, it clearly improves with JOURNAL OF THE AMERICAN WATER RESOURCES ASSOCIATION 1245 JAWRA

12 OLIVERA AND RAINA Figure 9. Coarse Resolution River Network of the Globe According to the NTM (based on a by grid). TABLE 6. Area of World Basins (km 2 ). Revenga Error Basin et al. (1998) NTM (percent) Amazon 6,144,727 6,045, Congo 3,730,474 3,942, Nile 3,254,555 3,429, Mississippi 3,202,230 3,365, Ob 2,972,497 3,010, Parana 2,582,672 2,902, Yenisey 2,554,482 2,686, Lake Chad 2,497,918 2,309, Lena 2,306,772 2,255, Niger 2,261,763 2,511, Amur 1,929,981 2,297, Mackenzie 1,743,058 1,817, Yangtze 1,722,155 2,242, Irtysh (Ob) 1,673,470 1,620, Madeira (Amazon) 1,485,218 1,478, Volga 1,410,994 1,334, Zambezi 1,332,574 1,371, Missouri (Mississippi) 1,331,810 1,439, Paraguay (Parana) 1,168,540 1,051, Nelson 1,093,442 1,247, Indus 1,081,733 1,131, St Lawrence 1,049,621 1,066, Ganges 1,016,104 1,106, Note: Only basins larger than 1,000,000 km 2 have been included. NTM refers to estimated values with a grid resolution of by respect to Olivera et al. (2002), Arora and Boer (1999), and O Donnell et al. (1999) (see Table 9). CONCLUSIONS The Network Tracing Method (NTM) has been developed to determine coarse gridded river networks for water resources modeling at a global, continental, and/or large basin scale. For each cell of a coarse resolution grid, the NTM determines its downstream cell and a meandering factor which helps improve the calculation of stream lengths. The NTM uses fine resolution vector stream data as the source of information of the flow patterns rather than DEMs as other upscaling methods do. The main advantage of using vector river networks as input is that they capture the hydrologic terrain features better than topographic data do and that they are easier to trace once they leave the cell for which the flow direction is being determined. Overall, the method captured the flow patterns well. Generated stream lines and drainage divides did not show major disagreements with those obtained from existing maps, most of which were consistent with the resolution of the coarse river network. Estimated basin areas, although close to documented values, were overpredicted, especially in the case of large basins. On the other hand, river lengths calculated with the NTM were consistently underpredicted, although an improvement was made when meandering factors, a unique feature of this method, were implemented. JAWRA 1246 JOURNAL OF THE AMERICAN WATER RESOURCES ASSOCIATION

13 DEVELOPMENT OF LARGE SCALE GRIDDED RIVER NETWORKS FROM VECTOR STREAM DATA TABLE 7. Length of World Rivers (km). NTM Not Using Meandering Factors Using Meandering Factors HYDRO1K Error Error River Length Length (percent) Length (percent) Nile 6,423 4, , Mississippi 5,337 3, , Yangtze 5,010 4, , Congo 5,003 3, ,785-4 Yenisey 4,993 3, , Huang He 4,863 2, , Amazon 4,766 3, ,320-9 Armur 4,559 4, ,288-6 Mekong 4,534 1, , Ob 4,482 3, , Lena 4,472 4, ,299-4 Niger 3,818 3, , Mackenzie 3,720 3, , Note: Only rivers longer than 4,000 km have been included. NTM refers to estimated values with a grid resolution of by TABLE 8. Comparison of River Network Methods (drainage areas in million km 2 ). Predicted Arora Revenga Olivera and Boer Basin et al. (1998) NTM et al. (2002) (1999) Congo Niger TABLE 9. Comparison of River Network Methods (side to corner ratios). Predicted Arora Olivera and O Donnell Balanced et al. Boer et al. Area Distribution NTM (2002) (1999) (1999) with balanced flow direction distributions are desirable because they are less likely to be affected by the orientation of the underlying grid than those with unbalanced distributions. The NTM also provides the capability of extracting stream length information from fine resolution networks and use it for estimation of river lengths with the coarse networks. Accurate evaluation of the flow distance from the cells to their downstream cells is necessary for travel time estimation for gridded flow transport modeling. For these reasons, we believe that the NTM provides an excellent alternative for developing coarse gridded river networks and setting up gridded flow routing models. Future work will focus on improving the algorithm that calculates the meandering factors to produce better river length estimations and on implementing the NTM for gridded flow transport modeling. Africa 59:41 59:41 64:36 72:28 Congo 59:41 59:41 62:38 79:21 74:26 Niger 59:41 59:41 62:38 70:30 72:28 The NTM improves the determination of gridded river networks with respect to previously developed upscaling methods because it generates networks in which all possible flow directions are equally likely to occur. This type of network is said to have balanced flow direction distributions. Gridded river networks ACKNOWLEDGMENTS This research has been conducted with support from the Department of Civil Engineering of Texas A&M University through the Research Innovation Program. The authors would like to thank the three anonymous reviewers of this manuscript for their valuable comments and input. Likewise, the contributions of Texas A&M University graduate students Elizabeth Bristow and Ashish Agrawal are appreciated. JOURNAL OF THE AMERICAN WATER RESOURCES ASSOCIATION 1247 JAWRA

14 OLIVERA AND RAINA LITERATURE CITED Arora, V. K. and G. J. Boer, A Variable Velocity Flow Routing Algorithm for GCMs. Journal of Geophysical Research 104(D24): Coe, M.T., Simulating Continental Surface Waters: An Application to Holocene Northern Africa. Journal of Climate 10: DeGroot, M. H., Probability and Statistics. Addison-Wesley Publishing Company, Reading, Pennsylvania. ESRI (Environmental Systems Research Institute), Cell- Based Modeling With Grid 6.1: Supplement Hydrologic and Distance Modeling Tools. ESRI Inc., Redlands, California. ESRI (Environmental Systems Research Institute), Digital Chart of the World. ESRI Inc., Redlands, California. Fekete, B. M., C. J. Vörösmarty, and R. B. Lammers, Scaling Gridded River Networks for Macro-scale Hydrology: Development and Analysis. Water Resources Research 37(7): Gesch, D. B., K. L.Verdin, and S. K. Greenlee, New Land Surface Digital Elevation Model Covers the Earth. Eos Trans. AGU 80(6): Graham, S. T., J. S. Famiglietti, and D. R. Maidment, Five- Minute, 1/2, and 1 Datasets of Continental Watersheds and River Networks for Use in Regional and Global Hydrologic and Climate System Modeling Studies. Water Resources Research 35(2): Hagemann, S. and L. Dümenil, A Parameterization of the Lateral Waterflow for the Global Scale. Climate Dynamics 14: Liston, G., Y. Sud, and E. Wood, Evaluating GCM Land Surface Hydrology Parameterizations by Computing River Discharges Using a Runoff Model: Application to the Mississippi Basin. Journal of Applied Meteorology 33: Miller, J., G. Russell, and G. Caliri, Continental Scale River Flow in Climate Models. Journal of Climate 7: O Donnell, G., B. Nijssen, and D. P. Lettenmaier, Simple Algorithm for Generating Streamflow Networks for Grid-Based, Macroscale Hydrological Models. Hydrological Processes 13: Oki, T. and Y. C. Sud, Design of Total Runoff Integrating Pathways (TRIP) A Global River Channel Network. Earth Interactions 2(2-001), 40 pp. Olivera, F., M. S. Lear, J. S. Famiglietti, and K. Asante, Extracting Low-Resolution River Networks From High-Resolution Digital Elevation Models. Water Resources Research 38(11):1231, doi:101029/2001wr Renssen, H. and J. Knoop, A Global River Routing Network for Use in Hydrological Modeling. Journal of Hydrology 230: Revenga, C., S. Murray, J. Abramowitz, and A. Hammond, Watersheds of the World. Water Resources Institute and Worldwatch Institute, Washington D.C. Sausen, R., S. Schubert, and L. Dümenil, A Model of River Runoff for Use in Coupled Atmosphere-Ocean Models. Journal of Hydrology 155: UNESCO, About the World Water Assessment Program. Available at index.shtml. Accessed on April 2, USGS (U.S. Geological Survey), Hydrologic Unit Maps. USGS Water-Supply Paper 2294, 63 pp. USGS (U.S. Geological Survey), 2003a. National Hydrography Dataset. Available at Accessed on April 4, USGS (U.S. Geological Survey), 2003b. National Elevation Dataset. Available at Accessed on April 4, Vörösmarty, C. J., B. Moore III, A. L. Grace, M. P. Gildea, J. M. Melillo, B. J. Peterson, E. B. Rastetter, and O. A. Steudler, Continental Scale Models of Water Balance and Fluvial Transport: An Application to South America. Global Biogeochemical Cycles 3(3): JAWRA 1248 JOURNAL OF THE AMERICAN WATER RESOURCES ASSOCIATION