HyG: A hydraulic geometry dataset derived from historical stream gage measurements across the conterminous United States

Regional- and continental-scale models predicting variations in the magnitude and timing of streamflow are important tools for forecasting water availability as well as flood inundation extent and associated damages. Such models must define the geometry of stream channels through which flow is routed. These channel parameters, such as width, depth, and hydraulic resistance, exhibit substantial variability in natural systems. While hydraulic geometry relationships have been extensively studied in the United States, they remain unquantified for thousands of stream reaches across the country. Consequently, large-scale hydraulic models frequently take simplistic approaches to channel geometry parameterization. Over-simplification of channel geometries directly impacts the accuracy of streamflow estimates, with knock-on effects for water resource and hazard prediction.

Here, we present a hydraulic geometry dataset derived from long-term measurements at U.S. Geological Survey (USGS) stream gages across the conterminous United States (CONUS). This dataset includes (a) at-a-station hydraulic geometry parameters following the methods of Leopold and Maddock (1953), (b) at-a-station Manning's n calculated from the Manning equation, (c) daily discharge percentiles, and (d) downstream hydraulic geometry regionalization parameters based on HUC4 (Hydrologic Unit Code 4). This dataset is referenced in Heldmyer et al. (2022); further details and implications for CONUS-scale hydrologic modeling are available in that article (https://doi.org/10.5194/hess-26-6121-2022). 

At-a-station Hydraulic Geometry

We calculated hydraulic geometry parameters using historical USGS field measurements at individual station locations. Leopold and Maddock (1953) derived the following power law relationships:

\(w={aQ^b}\)

\(d=cQ^f\)

\(v=kQ^m\)

where Q is discharge, w is width, d is depth, v is velocity, and a, b, c, f, k, and m are at-a-station hydraulic geometry (AHG) parameters. We downloaded the complete record of USGS field measurements from the USGS NWIS 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. 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 (QC) procedures in order to ensure the robustness of AHG parameters derived from the field data:

1. We considered only measurements which reported Q, v, w and A.
2. 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.
3. We excluded gages for which measured Q disagreed with the product of measured velocity and measured area by more than 5%. Gages for which  \( Q\neq vA\) are often tidally influenced and therefore may not conform to expected channel geometry relationships.
4. 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.
   1. We applied an iterative outlier detection procedure to the linear regression residuals. 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.
   2. Gages for which one or more regression had p-values >0.05 were excluded, as the relationships between log-transformed Q and w, v, or d lacked statistical significance.
   3. Gages were omitted if regressed AHG parameters did not fulfill two additional relationships derived by Leopold and Maddock: \(b+f+m=1{\displaystyle \pm }0.1\) and \(a{\displaystyle \times }c{\displaystyle \times }k=1{\displaystyle \pm }0.1\).
5. If the number of field measurements for a given gage was less than 10, either initially or after individual measurements were removed via steps 1-4, the gage was excluded from further analysis.

Application of the QC 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 QC.

At-a-station Manning's n

We calculated hydraulic resistance at each gage location by solving Manning's equation for Manning's n, given by

\(n = {{R^{2/3}S^{1/2}} \over v}\)

where v is velocity, R is hydraulic radius and S is longitudinal slope. We used smoothed reach-scale longitudinal slopes from the NHDPlusv2 (National Hydrography Dataset Plus, version 2) ElevSlope data product. We note that NHDPlusv2 contains a minimum slope constraint of 10^-5 m/m--no reach 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, and some Manning's n values we report may be inaccurate due to the NHDPlusv2 minimum slope constraint. We used median stream depth as an approximation for R, an assumption which 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. We used median v from the field measurement record for each gage. Thus, we report Manning's n values which approximately represent the historical median measured flow at each gage.

Daily discharge percentiles

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 QC:

1. For a given gage, we removed blocks of missing discharge values longer than 6 months. These long blocks of missing data generally correspond to intervals in which a gage was temporarily decommissioned for maintenance.
2. A gage was omitted from further analysis if its discharge record was less than 10 years (3,652 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 QC. 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.

HG Regionalization

We regionalized AHG parameters from gage locations to all stream reaches in the conterminous United States. This downstream hydraulic geometry regionalization was performed using all gages with AHG parameters in each HUC4, as opposed to traditional downstream hydraulic geometry--which involves interpolation of parameters of interest to ungaged reaches on individual streams. We performed linear regressions on log-transformed drainage area and Q at a number of flow percentiles as follows:

\(log(Q_i) = \beta_1log(DA) + \beta_0\)

where Q_i is streamflow at percentile i, DA is drainage area and \(\beta_1\) and \(\beta_0\) are regression parameters. 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 Q_99.9. Further discussion and additional analysis of HG regionalization are presented in Heldmyer et al. (2022).

Dataset description

We present the HyG dataset in a comma-separated value (csv) format. 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).