Consideration of Grid Cell Size to Represent Stream Networks for the Conterminous United States

Abstract

Recent modeling of groundwater at the scale of the Conterminous United States (CONUS) has often relied on relatively large square grid cells (Maxwell et al. 2015; Zell and Sanford 2020). Consequently, features such as streams can become generalized. An important issue, therefore, is the relationship between grid-cell size and representation of the stream network. This technical commentary addresses two questions related to this issue. First, what cell size is required to accurately represent all mapped streams in CONUS (McKay et al. 2012)? Second, given a 1-km cell, what order stream network can be accurately represented? This commentary focuses only on geometry and does not address other important aspects of modeling stream –aquifer interactions such as small-scale sinuosity (Cardenas 2009) or developing sound conceptual hydrogeologic models (Anderson et al. 2015).

The overall approach for assessing accuracy to answer these questions is presented in the methods section, including how the relationship between cell size and stream order is evaluated. The approach is applied to 18 representative surface water basins distributed across CONUS (Van Metre et al. 2020). The Delaware River Basin is used to illustrate the approach and for the purposes of discussion.

A uniform-square grid that accurately represents the geometry of a stream network is one in which contributing areas can be differentiated from streams, such that most of the cells do not contain a stream. A grid where every cell contains one or more streams would not accurately represent the geometry of the network. For the purposes of discussion, the criterion for accurate representation is that streams are in no more than 20% of all cells. A different criterion could be chosen depending on the purpose of a particular study. The graphs presented in this commentary allow for a different criterion.

The question of developing an accurate grid also depends on stream order. Representation of the geometry of a first-order stream network (headwaters) requires a smaller cell size than the representation of higher-order stream networks (large rivers). In this paper, we evaluate stream networks ranging from first through fifth stream orders across the CONUS.

The relationship between grid-cell size and stream network geometry is evaluated in 18 river basins distributed across CONUS (Figure 1; Table 1). These 18 river basins were identified as candidates for future intensive monitoring and assessment by the USGS (Van Metre et al. 2020) per a ranking scheme that represents the range of physiographic, climatic, and land use characteristics within CONUS. For each river basin, we used the Multi-Order Hydrologic Position (MOHP) dataset (Belitz et al. 2019; Moore et al. 2019) derived from the NHDPlusV2 stream network (McKay et al. 2012) as the basis for investigating the relationship between stream order and grid spacing. The MOHP provides a means for computing the distance of a point on the landscape to the nearest stream (DS) for a given stream order. The MOHP provides CONUS-wide, 30-m resolution metrics of lateral position (LP) and distance from stream to divide (DSD) for Thiessen watersheds (Johnston et al. 2009) of stream orders 1-9. For a given stream order, multiplying LP and DSD results in a DS for every 30-m pixel in a watershed. For this analysis, we compute the DS at the 18 representative river basins for stream orders 1-5 (Killian et al. 2024). With over 2.7 million stream reaches nationally, the number of reaches in the 18 river basins varies from under 8000 to over 86,000. The 18 river basins range in size from approximately 30,000 to 290,000 km², and therefore, the number of points used to characterize the distance of a point to a stream ranges from approximately 33 million to 326 million.

The Delaware River Basin is used to illustrate our approach to evaluating stream order and grid spacing. By Equation 1, using a 1-km grid spacing (x), the distance (d) where a 1-km grid cell will contain a stream is 707 m. With 250- and 100-m grid spacing, that distance is 177 and 71 m, respectively. Figure 2 shows the stream network for the Delaware River Basin, with the blue representing the Basin proportion where a 1-km grid will contain first-, third-, or fifth-order streams.

By computing the cumulative distribution function of DS for a given stream order (Figure 3), we can determine the river basin proportion where 1-km grid cells contain streams. For example, in the Delaware River Basin, the Basin proportion in which 1-km grid cells intersect a stream ranges from 72% for 1st order streams to 6% for 5th order streams (Figure 3; Table 2). In contrast, for 100-m grid discretization, the proportion of grid cells that intersect a stream ranges from 11% for 1st order streams to 2% for 5th order streams (Figure 3; Table 2).

The methods demonstrated on the Delaware River Basin are applied to 18 river basins shown in Figure 1. Cumulative distribution functions for each basin are computed and shown in Figure S2. The proportion of each river basin where 1-km grids contain streams is listed in Table S1, and their distributions are shown in Figure 4a for stream orders 1–5. The median river basin proportion where a 1-km grid contains a first order stream is approximately 70% across the 18 river basins. The median value where 1-km grids contain second order streams is approximately 30%. For third order streams, the median value where 1-km grids contain a stream is less than 20%, with exceptions for river basins with the densest stream networks: Lower Tennessee River, Lower Mississippi—St. Francis River, and San Joaquin River.

Figure 4b and 4c show the river basin proportions where 250- and 100-m grids contain streams for stream orders 1-5. For the 18 river basins across CONUS, the median river basin proportion for 250-m grids (Figure 4b) ranges from 25% for first-order streams to 2% for fifth-order streams. The median river basin proportion where 100-m grids contain first-order streams is about 10%. River basin proportions for combinations of grid spacing (1 km, 250 m, and 100 m) and stream order (1-5) for 18 river basins are in Table S1.

We assessed the accuracy of using grids of various sizes to represent stream networks in 18 representative surface water basins distributed across CONUS. Within each basin, we evaluated the accuracy of three different grid cell sizes: 1 km, 250 m, and 100 m. Within each basin, we evaluated stream networks from order 1 through order 5. As a criterion of accuracy, we assumed that a grid should contain less than 20% stream cells, and based on this criterion, a 1-km grid accurately represents the fourth-order stream network. To accurately represent the first-order stream network, a grid spacing of 100 m or less is required. If a criterion other than 20% was chosen, then the approach presented in this technical commentary could be used to address questions related to accurate grid representation of stream network geometry.

The authors do not have any conflicts of interest or financial disclosures to report. Any use of trade, firm, or product names is for descriptive purposes only and does not imply endorsement by the U.S. Government.