Xinhao Wang and Zhi-Yong Yin

An Evaluation of Using ArcInfo to Extract Basin Physiographic Parameters from DEMs

Characteristics of drainage networks and drainage basin physiographic parameters have been used widely in hydrologic calculation and modeling. Automated generation of drainage networks have become increasingly popular with the use of GIS and availability of Digital Elevation Models (DEMs). This study presents an effort to explore the capability of ArcInfo in generating drainage networks and extracting various drainage basin physiographic parameters. Twenty basins ranging from 150 km² to 1,000 km² in West Virginia, a geologically complex region, were examined in this study. It was assumed that the generated networks based on the 1:24,000 DEMs can fully represent the network characteristics. This assumption was verified by comparing the networks derived from the 1:24,000 DEMs with the US Geological Survey 1:100,000 Digital Line Graph (DLG) stream networks. The networks and basin parameters based on the 1:250,000 DEMs were then compared with those based on the 1:24,000 DEMs. Basin parameters commonly used in hydrology and geomorphology were examined, including drainage density, stream frequency, stream length, relief ratios, ruggedness number, and slopes. The purpose of this study is to evaluate the feasibility of using 1:250,000 DEMs for small to medium sized basins. Although 1:24,000 DEMs should render better results than the 1:250,000 DEMs, the use of the latter usually takes less resources and processing time. In addition, a complete coverage of the 1:250,000 DEMs for the United States is available on-line free of charge. It is recognized that the DLG data do not include true first-order streams if they do not have streamflows. However, it is our intention to focus on these streams represented on the DLGs because they have well defined drainage basins and valleys. As these streams carry significant amount of flows, they are important in water resources planning and management. The results show that the goodness-of-fit between the parameters based on 1:250,000 DEMs and 1:24,000 DEMs varies among different types of basin parameters and the 1:250,000 DEMs may be used to enhance computing efficiency in drainage basin analysis.

INTRODUCTION

Started with R.E. Horton (1945) and A.N. Strahler (1957, 1958, 1964), basin physiographic characteristics have long been believed to be important indices of surface processes. These parameters have been used in various studies of geomorphology and surface-water hydrology, such as flood characteristics, sediment yield, and evolution of basin morphology (Jolly, 1982; Ogunkoya et al., 1984; Aryadike and Phil-Eze, 1989; Breinlinger et al., 1993; Jensen, 1991). By including basin characteristics such as elevation and main channel gradient, predictions of stream discharge were substantially improved in comparison to using only drainage area andprecipitation (McArthur and Hope, 1993). More recently, terrain characterization became an important part in modeling surface processes (Nogami, 1995).

From the time when the methodology of basin analysis was first developed, it has been known for its tediousness and labor intensity. Most measurements must be made manually on large- to medium-scale topographic maps. Besides a few parameters that can be easily measured, such as elevation and relief, any attempt to get more complex parameters, such as stream length, drainage density, mean basin elevation and slope, and channel gradient for streams of different orders, was always hampered by the amount of work an analyst has to endure. This shortcoming has seriously limited the potential applications of drainage basin analysis in hydrology and geomorphology. Many have questioned the efficiency for models or methods that relies on accurate measurement of terrain characteristics because the improvements in model performance often do not justify the time spent in deriving these parameters (Pitlick, 1994).

Since the mid-1980s, with increased popularity of GIS technology and availability of Digital Elevation Models (DEMs), the potential of using DEMs in studies of surface processes has been widely recognized (Wharton, 1994). New methods and algorithms have been developed to automate the procedure of terrain characterization (Hogg et al., 1993; Guth, 1995; Desmet and Govers, 1996). DEMs have been used to delineate drainage networks and watershed boundaries, to calculate slope characteristics, and to produce flow paths of surface runoff (Moore et al., 1992; Quinn, et al., 1992; Tarboton et al., 1992; Wiche et al., 1992). In addition, DEMs have been incorporated in distributed hydrologic models (Garrote and Bras, 1995).

To use DEMs efficiently and appropriately, an important question needs to be answered: what is the best scale of DEMs for a given project? Obviously, this is determined by the size of the study area. For larger basins, smaller scale DEMs may be used to produce acceptable results. Even with today’s computing technology, the topography of a large basin represented by many large scale DEMs, e.g., 1:24,000, can easily reach the limit of computing power and storage space for most PC-based and even some workstation-based systems. Therefore, whenever possible, the smallest scale DEMs should be used to ensure computation efficiency as long as acceptable accuracy can be maintained. After examining the impact of DEM resolution on extracted drainage properties using hypothetical drainage network configurations, Garbrecht and Martz (1994) found that the response to DEM grid size varied among the extracted drainage properties. There is only limited discussion on the extent to which the DEMs of a given scale can be used to derive basin parameters with satisfactory accuracy.

This paper presents the results of a study on some of the most commonly used basin parameters derived from both the 1:24,000 (24K) and 1:250,000 (250K) DEMs for basins of different sizes (Table 1). Using the 24K DEMs as the standard, those parameters based on 250K DEMs were evaluated using statistical methods. Hopefully, results from this study will shed some lights on the limit and the type of basin physiographic parameters to which the smaller scale DEMs can still be used with acceptable accuracy. This will provide the basic knowledge to where and how the 250K DEMs should be used to increase data processing efficiency.

Table 1 Drainage network and basin parameters examined in this study (Strahler, 1964)

DATA

In this study, 20 drainage basins in West Virginia were examined. The State of West Virginia is located in the middle section of the Appalachian Highlands. The western part of the state is in the Appalachian Plateau Province, characterized by eroded terrains out of horizontal and slightly dipping strata. The eastern boundary of the Plateau is marked by major escarpments, with a sudden drop of elevation from more than 1000 meters to about 600 meters above the sea level. The eastern part of the state is in the "Newer" Appalachians Province, characterized by extensive ridge-and-valley topography with relief up to about 1000 meters. The underlying geologic structures are mostly eroded folds composed of sedimentary rocks of various ages (de Blij and Muller, 1996).

More than 30 basins up to about 1000 km² in size and with one or more US Geological Survey streamflow gaging stations were initially selected. The results of a study of DEM-derived basin characteristics and surface runoff will be reported in another paper. Fourteen 250K DEMs and more than two hundreds 24K DEMs were downloaded from a web site (poca.osmre.gov/data/index.html) maintained by the West Virginia Environmental Protection Department. With increasing basin size, it became more and more difficult to find basins entirely confined in West Virginia. A few defective 24K DEMs and some missing 24K DEMs further reduced the number of basins used in this study. The final dataset contains 20 basins, ranging from 153 km² to 1017 km² (Fig. 1). For the largest basin in this group, Little Kanawha River (LKR) basin, a total of seventeen 24K DEMs were assembled to cover the entire basin.

ArcInfo coverages based on Digital Line Graph (DLG) stream networks and watersheds at the 1:100,000 scale (100K) were also obtained from the previously mentioned web site. The DLG stream networks were used as the basis for comparison of DEM-derived drainage networks. The watershed coverage was used to define the boundaries for the selected basins.

METHODS

Initial Processing

The basin boundaries from the 100K watershed coverage were used to clip stream networks from the 100K stream network coverages. In this study, therefore, the basin area was predetermined. Then the 100K stream network and basin boundary coverages were converted into ArcInfo grids with two grid cell sizes corresponding to the 24K and 250K DEMs. The DEMs in these two scales were converted into ArcInfo lattices. Since the geographic coordinates of the 250K DEMs were in decimal seconds, they were first projected to the projection of the 24K DEMs and 100K DLGs - Universal Transverse Mercator (UTM) projection in Zone 17 with units in meters. The DEM lattices were then merged together and clipped by the basin boundaries to obtain a single DEM lattice for each basin. Finally, the DEM lattice was filled to create a seamless elevation lattice for a given basin. The ground resolutions were 30 meters for the 24K and 92.474 meters (3-second arc) for the 250K DEMs, respectively.

Generating Drainage Networks

The ArcInfo commands to create a stream network grid require the user to specify a value of cell numbers. Any cell in the flow accumulation grids with a value greater than this user-defined value will be included in the stream network. In other words, this value defines the minimum upstream drainage area necessary to maintain a stream. We could not find any discussion in the literature regarding how to set this value. Since the purpose of this study was to compare the DEM files at the two scales, we decided to use the stream length obtained from the 100K stream network coverages as the criterion. This was to ensure that the stream networks generated from DEMs of the two different scales are comparable. To implement this idea, we wrote an AML program to create stream grids with different cell numbers and to search for the value with whichthe 24K DEM-derived stream length was closest to the 100K stream length. Once the cell number for the 24K DEM (N_24K) was determined, the cell number for the 250K DEM (N_250K) was then computed as:

N_250K = N_24K*(C_24K/C_250K),

where C_24K and C_250K were the cell size of the 24K and 250K DEMs, respectively. The procedure was based on the assumption that the minimum area required to support the smallest stream segments of the drainage networks should be the same at both scales.

Once the stream network grid was created, we used the Horton-Strahler's drainage order approach to create a new stream network grid with stream orders (Strahler, 1964). This method counts stream orders from the head water tributaries. Stream order increases by one only when two tributaries with the same order meet at the confluence. For example, two first order streams meet to make a second order stream. The stream order grid was then converted into a network coverage with the ArcInfo vectorizing command.

The DEM lattices were used to create slope grids for the basins. The slope grids were then overlaid on the stream network grids to create a series of slope grids along the first order and all other order streams. In this way, channel gradients were estimated. Inversely, grids of slopes outside stream channels were also created.

Two groups of interim files were created for further analysis: 1) ArcInfo coverages, such as drainage basins and networks at the 1:24,000, 1:100,000, and 1:250,000 scales; and 2) ArcInfo grids, such as 24K and 250K elevations, slopes, and stream networks. These files are described in Table 2.

As previously mentioned, those basin parameters listed in Table 1 represent some of the most common characteristics of basin physiographic morphology. After the data files were produced at both the 1:24,000 and 1:250,000 scales for all the basins, the basin parameters were extracted from either the grids or the coverages. Actual procedures are summarized in Table 3.

Table 2 Interim files produced by ArcInfo*

* The files are arranged approximately in the direction of processing. Each basin has the same set of files.

Table 3 Procedures to Extract Basin Parameters

Evaluation of the Basin Parameters

We first performed paired Student-t tests on the means of the 24K and 250K basin parameters. The null hypothesis was that there was no difference between the means from the two groups. Results from the Student-t tests can provide information on how much on average the 250K DEMs over- or under-estimate the basin parameters. If the difference is not statistically different from zero at the 0.05 significance level, then it is possible to use the 250K parameters directly as the substitutes of the 24K parameters.

Linear regression was also used to examine how well were the 250K DEMs represent basin physiographic characteristics compared to the 24K DEMs. In regression, it is defined that:

BP_24K = a + b*BP_250K,

where BP_24K and BP_250K represent a given basin parameter extracted from 24K DEMs and 250K DEMs, respectively. For example, if the 250K DEMs can accurately portray the basin physiographic characteristics, then the parameter calculated using the 250K DEMs should be similar to that calculated using the 24K DEMs. In this case, a high coefficient of determination or R² value, a small constant term (a) that is not significantly different from 0 statistically, and a regression coefficient (b) very close to 1.0 are expected. In other words, the 250K DEMs can be directly used to extract the basin parameter as accurately as the 24K DEMs.

If the R² value is somewhat lower, but the constant term is still small and regression coefficient close to 1.0, the 250K DEMs can still be used to represent the basin parameter for multiplebasins to produce an unbiased estimate of the mean value; even though we may not be able to precisely estimate the basin parameter for individual basins with the 250K DEMs. This would be applicable in situations where regional characteristics are of interest. The third case is when the R² value is high, but the constant term is not significantly different from 0, nor is the regression coefficient close to 1.0. This means that the 250K DEMs consistently over- or under-estimate the parameter. However, there exists a strong relationship between the parameters estimated by the 24K and 250K DEMs. Based on such a relationship defined by regression analysis, the parameter based on the 250K DEMs can be readily transformed into the more accurate expression. Under a similar condition but with a lower R² value, the linear transformation must be used to give an unbiased estimate of the mean parameter value for multiple basins, but not for individual basins. Finally, if the R² value is very low, then it can be concluded that the 250K DEMs are not suitable to estimate the basin parameter, and there is no other option but to use the 24K DEMs.

RESULTS AND ANALYSIS

Visual Evaluation of the Networks

Fig. 2 is a map of Upper Green River basin, one of the 20 basins examined in this study. DEM-derived stream networks at both scales resemble closely the general shape and pattern of the 100K DLG streams. Similar results were found for most basins examined. Obviously, the streams based on the 24K DEMs matched the DLG streams very well, even for small details of the networks. On the other hand, the streams based on the 250K DEMs appeared as short straight segments and often located slightly off the 100K DLG streams. Another observation is that the DLG streams extended longer than the DEM streams at the head water, while the DEM streams had some tributaries that were not shown in the DLG networks. One of the problems we encountered was that some of the DEM-generated stream networks were discontinuous within the basin boundaries. Four 24K basins and seven 250K basins had this problem that might be partially resulted from the complex geologic and topographic conditions in the study area. Another possible cause was the lack of topographical variation at certain locations in the basins. The flow direction could not be determined due to a relatively low vertical resolution of the DEMs. This problem should be more relevant to the 250K DEMs. These results indicate that it should be careful to use the 250K DEM generated streams in any analysis requiring accurate flow directions. Also the drainage basins delineated entirely using DEMs may not be accurate in some cases. However, these stream networks should provide a fairly good basis for calculating certain basin characteristics.

Characteristics of the Networks

Several network characteristics were compared, including total stream length, main stream length, and stream frequency and sum of stream length by stream orders. Since the total stream length from the 100K DLG streams was used as the standard in network generation process, both the 24K and 250K networks should have virtually the same values. However, results of the paired Student t test indicated that the 250K DEMs still underestimated total stream length.While the difference between the means was small (420 km by the 250K DEMs versus 453 km by the 24K DEMs), it was statistically significant (p = 0.0001). Similarly, the 250K DEMs underestimated drainage density as the same basin area values were used for both 24K and 250K scales (Table 4).

Table 4 Paired Student t test on Characteristics of the Networks

¹ Significance level or the greater-than or equal-to probability of the t value

* Significant at the 0.05 level

The main stream length usually varies between the two scales because the details of the networks may be different. As mentioned earlier, 7 basins had discontinuous networks within the pre-determined basin boundaries. The comparison of main stream lengths from the remaining 13 basins showed that the 250K DEMs again significantly underestimated this parameter (Table 4).

Although the 250K DEMs underestimated the above network parameters, regression analysis results suggested that the DEMs could still be used to provide precise estimates for individual basins after linear transformations (Fig. 3). The coefficients of determination or R² values of the three regression models range from 0.90 for drainage density to 0.98 for total stream length (Table 5).

Similar results were found for the sum of stream length by stream order. The 250KDEMs underestimated stream length for all orders, although the statistical significance was not as prominent as in the case for the entire networks (Table 4). Again regression models could be used to provide precise estimates, but only for the first, second, and third order stream lengths (Table 5). For higher order streams (fourth and fifth), the R² values were significantly lower (0.71 and 0.69), probably due to the effect of fewer streams having higher orders (Fig. 4).

Stream frequencies by stream order were used as the criterion for comparing topological characteristics of the networks. Frequencies by stream order were first compared between the networks of the two scales by the paired Student t test. In general, the 250K DEMs tended to produce fewer stream segments than the 24K DEMs (Table 4). Only for the fifth order streams, the 250K DEMs produced slightly more stream segments than the 24K DEMs and the difference was not statistically significant. This implied that the number of nodes and links of the two sets of networks should also be very similar. This was confirmed by the results of regression, although the degree of goodness-of-fit reduced when stream order was higher than 3 (Table 5, Fig. 5).

Table 5 Regression analysis on Characteristics of the Networks

* Significant at 0.05 level

Basin Parameters Based on Drainage Network and DEMs

Paired Student t test indicated that the 250K DEMs tended to underestimate basin elevation variability (Table 6). Obviously, some high or low elevation points might simply be missed due to the larger ground resolution cell size of the 250K DEMs. Results of regression analysis, however, again indicated that the 250K DEMs can give very good estimates to those parameters based on elevations, such as mean, maximum and minimum basin elevations, and basin relief (Table 7). The R² values were higher than 0.98, indicating almost perfect linear relationships (Fig. 6). Similarly, the 250K DEMs could be used to provide accurate estimates of relief ratio and the ruggedness number (Table 7, Fig. 7). As the calculation of relief ratio was based on both main stream length and basin relief, only those basins with continuous networks were compared.

Table 6 Paired Student t test on elevation- and slope-based parameters

* Significant at 0.05 level

Table 7 Regression analysis on elevation- and slope-based parameters

* Significant at 0.05 level

(Figure 6)

(Figure 7)

Slope parameters based on the 250K DEMs were consistently underestimated comparing with the 24K DEMs (Table 6). The highest R² value of the regression models for the slope-based parameters was found for the mean gradient along first order streams (R²=0.82), while the R² values for mean and maximum basin slopes were in the range of 0.6-0.7 (Fig. 8). The mean slope outside stream channels was virtually the same as the mean basin slope. The R² values for other slope-based parameters were much lower. This was resulted from the generalized terrain variation with the decreased resolution of the 250K DEMs. Therefore, the 250K DEMs could only make fair estimates for some slope parameters, such as mean and maximum basin slope, mean gradient of first order streams, and mean slope outside stream channels, after the linear transformation. The best usage was to derive regional average values for multiple basins rather than for individual basins. For some parameters, such as the maximum gradient of first order streams and mean channel gradient of second or higher order streams, the 250K DEM could only give poor estimates. The 250K DEMs were useless for maximum channel gradient of second or higher order streams. Unlike other slope-based parameters, the 250K DEMs overestimated relief ratio, a measure of average gradient along the main stream. The 250K DEMs underestimated both basin relief and main stream length, but the latter was underestimated to a greater extent than the former parameter. So the ratio calculated from the 250K DEMs became higher than that from the 24K DEMs.

CONCLUSIONS

In this study, stream networks were constructed using both 24K and 250K DEMs and various drainage basin physiographic parameters were extracted from the DEMs and the networks. The complex geologic and topographic conditions in West Virginia certainly offered challenges to both the authors and the software/hardware configuration. One the other hand, however, such complexities also enhance the validity of the study results in the sense that the findings may be applicable under a wide variety of conditions.

Under a well-controlled condition using total stream length as the criterion to generate drainage networks, the 250K DEMs performed very well against the 24K DEMs. The general shape and even some of the details of the drainage networks as well as some simple topological parameters all appeared to match closely. Some of the basins did not have continuous networks, although this problem was not unique to the 250K DEMs. It is possible to fix the problem by decreasing the area required to generate the first order streams.

When comparing basin physiographic parameters extracted from both 24K and 250K DEMs, wefound that the 250K DEMs were best used to estimate various elevation-based parameters. The differences between the mean parameter values of the two groups of basins were usually statistically significant as revealed by paired Student t tests. Therefore, it might not justify to use the 250K parameters directly as the substitutes of the 24K parameters. However, regression analysis revealed strong linear relationships with very high R² values. In most cases, more than 90% of the variation in the 24K parameters were explained by the 250K parameters. We were less confident about the slope- or gradient-based parameters. The 250K DEMs tended to consistently underestimate almost all the slope measurements. Even with linear transformation based on regression models, the 250K DEMs might only be able to provide fair estimates for some parameters (with R² values typically in the range of 0.6-0.8), such as basin slope and first order stream channel gradient; for others, such as channel gradient of second or higher order streams, the accuracy was even lower (R² values lower than 0.5).

It should be pointed out that the stream networks based on the 100K DLG files may not include the true first-order streams. Mostly those stream lines indicate streams with perennial flows, or at least with intermittent flows. The resulted networks based on the DEMs in this study, therefore, also have the same nature. However, this should not diminish the importance of this study. The streams displayed in the 100K DLG networks tend to have well defined valleys and drainage areas. The basins of these streams can be considered as tangible geomorphic units. Since these streams carry significant amount of stream flow during the year, they are important in water resources planning and management.

Further studies are required to investigate how universal are those linear relationships between the parameters derived from 24K and 250K DEMs. If such relationships can be reproduced in other regions with similar geologic and topographic settings, then the 250K DEMs may be used to enhance computing efficiency in drainage basin analysis. Additionally, the impact of geologic and topographic complexities to the accuracy of the DEM-derived networks needs to be investigated.

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Dr. Zhi-Yong Yin
Associate Professor, Department of Geography
Georgia State University
Atlanta, GA 30303
Telephone: (404) 651-1826
Fax: (404) 651-3235
E-Mail: gegzyy@panther.gsu.edu