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Scientific Data volume 11, Article number: 1153 (2024 ) Cite this article eaton vickers
Regional- and continental-scale hydrologic models are increasingly important forecasting tools, yet they rely on highly variable channel parameters (e.g. width, depth, hydraulic resistance) that remain unquantified for millions of stream reaches across the country. Existing hydrologic models utilize over-simplified channel geometries that directly impact the accuracy of streamflow estimates, with cascading effects for water resource and hazard prediction. Here, we present a hydraulic geometry dataset, termed ‘HyG’, derived from discharge field measurements at U.S. Geological Survey (USGS) stream gages across the conterminous United States (CONUS). The HyG dataset includes (1) at-a-station hydraulic geometry parameters, (2) at-a-station hydraulic resistance (Manning’s n) calculated from the Manning equation, (3) daily discharge percentiles, and (4) regionalized downstream hydraulic geometry parameters based on HUC4 (Hydrologic Unit Code 4), derived from a total of 4,051,682 individual measurements from 66,841 total gages. The regionalized HyG dataset can be used directly to improve channel representations in models over CONUS. The original HyG relationships can also be regionalized for finer scales if required.
Considerable uncertainties in the channel dimensions and hydraulic roughness used in regional- and continental-scale hydrologic models are important sources of errors in predicted flood volumes and peak flow timing1. Channel properties that are critical to hydraulic and hydrologic modelling—including slope, cross sectional area at different flows, hydraulic resistance, and reach length—are minimally constrained for most river systems. For example, of the ~2.7 million river reach segments in the NOAA (National Oceanic and Atmospheric Administration) National Water Model (NWM), channel properties have been measured for only ~2,800 reaches. Even with a perfect hydrologic simulation, uncertainties in channel properties can lead to errors in hydrologic predictions, particularly those related to the speed and timing of flood flows1. There is therefore a need for observation-based estimates of channel properties which can improve the realism of streamflow simulations in the NWM and other models where river routing takes place (e.g. River Transport Model2, mizuRoute3, Model for Scale Adaptive River Transport4). To that end, we present a new dataset of hydraulic geometry parameters, called ‘HyG’, derived from a repository of over 4 million historical U.S. Geological Survey (USGS) field measurements at over 66,000 stream gage locations in the conterminous US. This dataset is provided to enhance the representation of stream channels in current and future regional- and continental-scale streamflow modelling efforts. Data from HyG have already been leveraged for improved streamflow prediction within the NWM1. In addition to hydraulic geometry parameters, as part of HyG, we provide sample calculations of hydraulic resistance (Manning’s n) and an example regionalization method at the HUC4 (Hydrologic Unit Code 4; USGS-designated subregion scale (average HUC4 size ~ 40,000 km2)) scale using discharge and drainage area.
During routine field discharge measurements undertaken by water agencies, such as the USGS, the agency operator collects the stream channel measurements of width, cross-sectional area, and average velocity to calculate discharge. This method for stream field discharge measurement was standardized initially by the USGS in 1889, and field measurements have been taken regularly at gage locations across the U.S. ever since. These field measurements are generally taken at least every few months (i.e. several measurements per year); at many gages, measurements are taken more frequently and/or multiple measurements in the vicinity of the gage are taken on the same day. These under-utilized field discharge measurements are the best source of large-scale stream bathymetry and hydraulic data to date in the U.S. Even when remotely-sensed river observations of width, water surface elevation and slope are widely available for larger rivers —such as those from the NASA SWOT (Surface Water and Ocean Topography) Mission5— field measurements will remain a key component of hydrologic measurement, providing important calibration and ground truth information.
Stream hydraulic geometry (HG) was first defined by Leopold and Maddock6 and since has been refined by a large body of subsequent research7,8,9,10,11,12,13,14,15,16,17,18,19. At the heart of the hydraulic geometry argument is that power-law relationships can be used to describe the cross-sectional variation of stream discharge with width, depth, and velocity, known as at-a-station hydraulic geometry (AHG)
where w is the width of the water surface, d is depth to the channel bottom, v is velocity, Q is discharge, a and c and k are fitted coefficients, and b and f and m are fitted exponents. These AHG relationships stem from the standard calculation of stream discharge, whereby discharge is equal to the product of width, depth and velocity. Therefore, b + f + m = 1 and a × c × k = 1. Downstream hydraulic geometry (DHG) can be described with a similar set of power law relationships if discharge is held at a steady value (e.g. bankfull, median annual flow, 0.5 annual exceedance probability, etc.) and is used to describe the variation in width, depth and velocity moving downstream through the channel network.
A large body of research investigating the root causes, analytical solutions, and empirical relationships of hydraulic geometry7,8,9,10,11,12,13,14,15,16,17,18,19 has shown that the AHG relationships—and to a lesser extent the DHG relationships—generally replicate unmeasured within-bank channel morphology16,17,18. Local conditions, such as bedrock outcrops, human modification, etc., can cause deviations from the relationships. One of the more recent and commonly-used large compilations of field measured data, the ‘HydroSWOT’ database by Bjerklie et al.20, was collected using only acoustic Doppler current profiler (ADCP) records, which are skewed toward high-discharge rivers and events and do not well-represent smaller rivers or events. Another recent large compilation of field measured data by Afshari et al.19, investigated AHG relationships but did not investigate DHG or hydraulic resistance. In contrast to these previous efforts, our present effort aims to estimate within-bank AHG for stations with discharge field measurements, to combine with slope to estimate hydraulic resistance, and then to apply these relationships to estimate HG and resistance at unmeasured reaches.
A critical deficiency in the majority of stream channel databases used for hydrologic modelling over CONUS, such as the widely-used USGS National Hydrography Dataset (NHD), is that there is not enough information in the databases to calculate all the components of a 1D hydraulic solution. In particular, including longitudinal slope (e.g. downstream rise over run) for each gaged location, channel area over a range of flows, and velocity is critical, as it enables parameterization of hydraulic resistance. This is illustrated in the calculation of velocity in a reach using a standard flow-resistance equation, such as the Manning Equation, in which flow velocity, v, is determined by channel dimensions (hydraulic radius, R), slope, S, and hydraulic resistance, n:
For nearly all USGS and state stream gaging locations in the U.S., longitudinal slope has not been linked to the field discharge measurements for the gages in question, and hence hydraulic resistance cannot be calculated (one known variable and three unknowns in Eq. 4). As a result, hydraulic resistance often is guessed using rules-of-thumb from photographs21, using highly-detailed channel and grain size measurements that are unrealistic for large-scale hydrologic models22,23, or by using reach properties several steps removed from the reach hydraulic properties.
We calculated hydraulic geometry parameters (variables a, b, c, f, k, and m in Eqs. 1–3) using historical USGS discharge field measurements at individual station locations. We downloaded the complete record of USGS field measurements through the end of the 2018 water year (September 30, 2018) from the USGS NWIS (National Water Information System) portal (https://waterdata.usgs.gov/nwis/measurements). This raw dataset includes 4,051,682 individual measurements from a total of 66,841 stream gages within CONUS. Quantities of interest in AHG derivations are Q, w, d, and v (Eqs. 1–3). USGS field measurements do not include d—we therefore calculated d using d=A/w, where A is measured channel area. We applied the following quality control procedures in order to ensure the robustness of AHG parameters derived from the field data:
We considered only measurements which reported all of the following: Q, v, w and A.
We excluded individual measurements for which measured Q disagreed with the product of measured velocity and measured area by more than 5%. Gages at which Q≠vA are often tidally influenced or have multiple channels and therefore may not conform to expected channel geometry relationships.
We excluded all gages with fewer than 10 measurements. This removed 45,235 gages.
For each gage, we excluded measurements older than the most recent five years, so as to minimize the effects of long-term channel evolution on observed hydraulic geometry relationships. Representing the current channel geometry, as opposed to past conditions, is necessary to improve the accuracy of operational streamflow forecasting. Gages that passed this quality control step had a minimum of 10 measurements, with a mean of 30 measurements and a median of 28 measurements over the five-year interval
Q, v, w, and d from field measurements at each gage were log-transformed. We performed robust linear regressions on the relationships between log(Q) and log(w), log(v), and log(d). AHG parameters were derived from the regressed explanatory variables (e.g. Figure 1) using the following additional quality control steps:
Example calculation of AHG parameters from stream channel measurements at USGS gage 01010000. Log-transformed Q is regressed with log-transformed v, w, and d to calculate the parameters described in Eqs. 1–3.
We applied an iterative outlier detection procedure to the residuals of the linear best-fit regression equations. Values of log-transformed w, v, and d residuals falling outside a three median absolute deviation (MAD) envelope were excluded. Regression coefficients were recalculated and the outlier detection procedure was reapplied until no new outliers were detected. We emphasize that the outlier observations that are removed in this step are not outliers in terms of their flows (i.e. very high or low discharge). They are outliers in that they conform very poorly to the AHG relationships described by the other observations for the given gage.
At this stage, we re-screened based on number of measurements, excluding those gages for which the number had dropped below 10. This removed an additional 2,458 gages.
Gages for which one or more regressions had p-values > 0.05 were excluded, as the relationships between log-transformed Q and w, v, or d lacked statistical significance. 7,536 gages were removed at this step.
Gages were omitted if regressed AHG parameters did not fulfill two additional relationships derived by Leopold and Maddock6: b + f + m = 1 ± 0.05 and a × c × k = 1 ± 0.05. 99 gages were removed at this step.
Application of the procedures described above removed 55,328 stream gages, many of which were short-term campaign gages at which very few field measurements had been recorded. We derived AHG parameters for the remaining 11,513 gages which passed our quality control filters. The spatial distributions of filtered and retained gages are shown in Fig. 2.
Distribution of USGS stream gages across CONUS for which manual measurements exist. Red gages were included in the HyG database. Blue gages were screened out by our quality control procedures.
As part of the HyG database, we combined hydraulic geometry with reach longitudinal slope using the NHDPlusv2 (National Hydrography Dataset Plus, version 2) (https://www.epa.gov/waterdata/nhdplus-national-hydrography-dataset-plus) ElevSlope longitudinally-smoothed slope product. The resulting function for parameterizing reach-scale hydraulic resistance (in this case, also known as Manning’s n) can inform future operational streamflow modelling efforts. To our knowledge, this effort represents the first slope-based national-scale estimation of hydraulic resistance in the U.S.
We calculated hydraulic resistance at each gage location by solving the Manning Equation for Manning’s n (Eq. 4). We note that any errors in NHDPlusv2 ElevSlope will propagate into the Manning’s n values we calculate. For example, NHDPlusv2 contains a minimum slope constraint of 10−5 m/m—no reach in the database may have a slope less than this value. Furthermore, NHDPlusv2 lacks slope values for certain reaches. As such, we could not calculate Manning’s n for every gage.
Nearly all hydrologic models make the assumption that the energy slope is approximated by topographic channel slope. As such, we have used topographic channel slope (from NHD) in our calculations of Manning’s n. We note that, while Manning’s n can be calculated from any of the estimated discharge exceedance probabilities, the most reasonable results will likely be obtained from flows representing in-channel flow under normal (i.e. not low or high extreme) conditions.
We thus report two Manning’s n values, both of which take stream depth as an approximation for hydraulic radius (R). The first (ndfm) takes the median stream depth and velocity measurements from the USGS’s database of manual flow measurements for each gage. The second (nQ50) uses stream depth and velocity calculated for a 50th percentile discharge (Q50; see Section 2.3). Approximating R as stream channel depth is generally considered valid if the width-to-depth ratio of the stream is greater than 10—which was the case for the vast majority of field measurements (Fig. 3). Thus, we report two Manning’s n values for each gage which are both intended to approximately represent median flow conditions.
Histogram of stream channel width-depth ratios in HyG gages. Over 95% of gages have width-depth ratios > 10.
We downloaded full daily discharge records from 16,947 USGS stream gages through the NWIS online portal. The data includes records from both operational and retired gages. Records for operational gages were truncated at the end of the 2018 water year (September 30, 2018) in order to avoid use of preliminary data. To ensure the robustness of daily discharge percentiles, we applied the following filters:
For a given gage, we removed blocks of missing discharge values longer than 6 months. Of the 16,947 gages, ~29% (4,984) had at least one missing block of discharge values. Most of these missing blocks were multi-year intervals during which gages were decommissioned for maintenance or other reasons. In certain gages, missing blocks of data represent seasonal shutdowns, often due to below-freezing temperatures in the area of the gage but also due to non-perennial streamflow. Such gages may yield less reliable daily discharge percentiles, as their streamflow records will be seasonally biased. However, only 271 gages (1.6%) had five or more such missing blocks. Thus, seasonally-biased gages do not exert a major influence on HyG.
A gage was omitted from further analysis if its discharge record was less than 10 years (3,650 days) long, and/or less than 90% complete (>10% missing values after removal of long blocks in step 1).
We calculated discharge percentiles for each of the 10,871 gages which passed the quality control filters. A discharge percentile of Q90 indicates a 90th percentile flow, which is only exceeded 10% of the time. This is equivalent to an annual exceedance probability of 10%. Discharge percentiles were calculated at increments of 1% between Q1 and Q5, increments of 5% (e.g. Q10, Q15, Q20, etc.) between Q5 and Q95, increments of 1% between Q95 and Q99, and increments of 0.1% between Q99 and Q100 in order to provide higher resolution at the lowest and highest flows, which occur much less frequently.
Making field measurements is infeasible at all ~2.7 million reaches in the NHD dataset, hence it is useful to identify regional values for the hydraulic parameters described above. To this end, we implemented a ‘regionalization’ strategy to identify reach properties at the national scale. We used the AHG relationships in the HyG database and USGS stream gage discharge records to regionalize stream properties at the HUC4 scale for a range of flow percentiles, as opposed to traditional downstream hydraulic geometry–which involves interpolation of parameters of interest to ungaged reaches on individual streams using only discharge6. Regionalization strategies such as this have the potential to significantly improve the realism of stream channel representations in hydrologic models. Heldmyer et al.1 pursued a similar strategy at the HUC2 level, in order to ensure a hydraulic geometry relationship for every HUC2.
For all gages in a given HUC4, linear regressions were performed on log-transformed drainage area from NHDPlusv2 and Q from USGS daily discharge records at a number of flow percentiles as follows:
where \({Q}_{i}\) is streamflow at percentile i, \({DA}\) is drainage area, and \({\beta }_{1}\) and \({\beta }_{0}\) are regression parameters. We thus derived regression relationships between streamflow and drainage area which were variable between low and high flows. Using NHDPlusv2 drainage area and our derived logQ-logDA regression coefficients, it is possible to calculate streamflow, velocity, width, depth, and Manning’s n for nearly all reaches in a HUC4, save for ~5% which lack a drainage area and/or longitudinal slope in NHDPlusv2. However, we note that certain HUC4s contained very few gages that passed QC (Fig. 4). Regionalization could not be performed for these HUC4s (n < 8), due to these low sample sizes.
HUC4s across CONUS colored by number of gages with both AHG parameters and daily discharge data. Regionalization could not be performed on HUC4s with very few (n < 8) gages. Gage locations are shown in grey.
As part of HyG, we report \({\beta }_{1}\) , \({\beta }_{0}\) , and the r2 value of the regression relationship for Q percentiles Q10, Q25, Q50, Q75, Q90, Q95, Q99, and Q99.9. Further discussion of HG regionalization and additional analysis are presented in Heldmyer et al.1 We deemed the above set of relationships sufficient for characterizing channel properties for the purpose of improving channel representations in CONUS-scale models. However, HUC4-scale regression relationships can easily be derived for the other Q percentiles we report (e.g. Q5, Q1, etc.) if they are of interest to the user, as we have provided the percentiles themselves and the associated drainage area.
The HyG dataset is available as a single table in comma-separated value (csv) format in the Zenodo public data repository (https://zenodo.org/records/10425392)24. Each row corresponds to a different USGS stream gage. Information in the dataset includes gage ID (column 1), gage location in latitude and longitude (columns 2-3), gage drainage area (from USGS; column 4), longitudinal slope of the gage’s stream reach (from NHDPlusv2; column 5), AHG parameters derived from field measurements (columns 6–11), Manning’s n calculated from median measured flow conditions (column 12), Q percentiles (columns 13–50), HG regionalization parameters and r2 values (columns 51–74), and geospatial information for the HUC4 in which the gage is located (from USGS; columns 75–86).
There is a substantial theoretical and practical basis for calculating the AHG parameters in HyG, having been established over 50 years ago and supported by decades of subsequent research7,8,9,10,11,12,13,14,15,16,17,18,19. The observational data from which the parameters were derived were collected in accordance with specific standards which have been established for over a century at the USGS. Furthermore, the rigorous quality control procedure we applied (see Section 2.1) ensures that only data from gages with high-quality, most recent observational records on reaches which are not tidally influenced or multi-channel are used in the derivation of AHG parameters. It is not possible to validate the AHG parameters we have derived against known nationwide benchmarks—because these have not been previously established. Instead, we present some goodness-of-fit statistics to support the robustness of the AHG parameters we have derived (Fig. 5). The mean r2 values of the relationships between log(Q) and log(v), log(w), and log(d) where 0.81, 0.71, and 0.83, respectively. The median r2 values were somewhat higher: 0.88, 0.76, and 0.89. Only ~10% of gages had r2 values < 0.5. The mean root mean squared errors of these relationships were 0.10, 0.07, and 0.08, respectively. The sound theoretical basis, high measurement standards, rigorous quality control, and statistical strength of our derived relationships increase our confidence in the technical quality of this dataset. Lastly, Heldmyer et al.1 found that stream channel parameterizations leveraging HyG resulted in improved streamflow performance in the NWM. Although these results are encouraging, further research leveraging HyG for streamflow modelling applications is necessary to fully validate the AHG parameters themselves.
r2 values at HyG gages for the log(Q):log(v) (top), log(Q):log(w) (middle), and log(Q):log(d) (bottom) AHG regressed relationships. Mean and median r2 and mean root mean squared error across all gages for each relationship are displayed in each panel.
Both Manning’s n fields included in HyG are intended to represent hydraulic resistance under approximate median flow conditions. However, Manning’s n can be calculated for any discharge or annual exceedance probability, including those found in the HyG dataset. The majority of Manning’s n values we calculated fall within the realistic range of Manning’s n values observed in natural river and floodplain systems (~0.02–0.08)21. The mean and median Manning’s ndfm values were 0.068 and 0.052, respectively (Fig. 6). The mean and median Manning’s nQ50 values were 0.111 and 0.066, respectively.
Distribution of Manning’s ndfm values for the gages in HyG. The approximate realistic range of n values is boxed in red. Most values falling below the realistic range correspond to gages on reaches with the NHDPlusv2 minimum slope constraint of 10−5 m/m. Values of Manning’s nQ50 exhibit a similar distribution (not shown).
We note that most low (<0.02) Manning’s n values occur on stream reaches where the NHDPlusv2 slope value is equal to the minimum slope constraint (10−5 m/m). Thus, the Manning’s n values we derived for these reaches may be biased by artificially low slopes. Users of the HyG dataset should exercise caution in using data from gages where the published NHDPlusv2 slope is equal to this minimum value.
Furthermore, both Manning’s n fields contain some unrealistically high outliers. Given that all the gages we included in HyG passed our quality control procedures, these values have been left in the database. Possible reasons for unrealistically high Manning’s n values include overly steep NHDPlusv2 slope values for the gages in question and measured channel depth being unrepresentative of hydraulic radius. The Manning equation is known to break down for certain channel types—particularly channels that are steep, shallow, and/or coarsely bedded25—and thus some spurious Manning’s n values are to be expected.
To validate our HUC4-based regionalization strategy, we performed an iterative drop-20 analysis of the logQ-logDA relationships. For each HUC4, we randomly excluded 20% of gages from the regression, calculating regression fit parameters using the remaining 80%. We then derived an expected Qi for each gage using the associated logDA and HUC4 regression parameters. Finally, we calculated the root mean squared difference (RMSD) between the observed and expected Qi of the withheld points (Fig. 7). We repeated this process 100 times, randomly re-selecting gages to be excluded in each iteration.
Example drop-20 analysis for HUC 0305. Regression parameters were calculated based on the white points. Regression misfit was evaluated by taking the RMSD between the withheld points (red) and predicted points (blue). The r2 of the regression and RMSD of the predicted points are shown. This plot represents a single iteration of the 100 iteration drop-20% analysis.
The drop-20 analysis revealed exceptionally strong logQ-logDA relationships in the eastern and northwestern U.S. (Fig. 8). These relationships are stronger at higher flows: at Q90, r2 values in these regions are generally >0.8, and RMSDs are <2 m3/s. y contrast, in the southern Great Plains, western U.S. mountains, and southwestern deserts, the logQ-logDA relationship is much weaker, which may reflect issues related to hydroclimatology or the extensive active water management across these regions. Overall, logQ-logDA relationships exhibit relatively strong relationships which improve with increasing flows (Table 1).
(top) r2 values for the logQ-logDA regression relationship at Q90 at the HUC4 scale. (bottom) RMSD of the logQ-logDA drop-20 analysis at Q90.
We do not intend for the regionalization strategy we have pursued to be considered the single ‘best’ regionalization strategy for all purposes. Regionalization can be carried out based on different criteria (e.g. Q-slope vs. Q-DA) and should be explored at different spatial scales to suit the needs of each project. We present this example regionalization as part of the HyG dataset, but it should not prevent users from developing their own regionalization schemes using the other components of HyG. As noted above, additional discussion of regionalization is available in Heldmyer et al.1
The workflow used to curate the HyG dataset was developed in Matlab. This code is publicly available at github.com/then6702/HyG
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This material is based upon work supported by the NSF National Center for Atmospheric Research, which is a major facility sponsored by the U.S. National Science Foundation under Cooperative Agreement No. 1852977. This research was also supported by the National Oceanic and Atmospheric Administration, Office of Atmospheric Research, Joint Technical Transfer Initiative (grant no. NA18OAR4590391).
Research Applications Laboratory, NSF National Center for Atmospheric Research, Boulder, USA
Cooperative Institute for Research in Environmental Sciences, University of Colorado Boulder, Boulder, USA
J. Toby Minear & Ben Livneh
Department of Civil, Environmental, and Architectural Engineering, University of Colorado Boulder, Boulder, USA
Western Water Assessment, University of Colorado, Boulder, Boulder, USA
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Dr. Tom Enzminger performed the majority of the technical and written work described in this manuscript, including derivation of AHG parameters and daily discharge percentiles and HG regionalization. Dr. Toby Minear provided supervision and guidance, as well as subject matter expertise on hydraulic geometry and hydraulics in river channels. Dr. Ben Livneh provided guidance related to hydrologic models and the utilization of channel properties by those models.
Correspondence to Thomas Enzminger or J. Toby Minear.
The authors declare no competing interests.
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Enzminger, T., Toby Minear, J. & Livneh, B. HyG: A hydraulic geometry dataset derived from historical stream gage measurements across the conterminous US. Sci Data 11, 1153 (2024). https://doi.org/10.1038/s41597-024-03916-7
DOI: https://doi.org/10.1038/s41597-024-03916-7
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