Accurate representation of channel properties is important for forecasting in hydrologic models, as it affects the height, celerity, and attenuation of flood waves. Yet, considerable uncertainty in the parameterization of channel geometry and hydraulic roughness (Manning's

In the continental United States (CONUS), flood events are among the most significant natural disasters in terms of damage to life and property. Direct losses from flooding rank a close second to hurricanes and represent a quarter of nationwide total damages stemming from natural hazards at USD 144 billion in losses from 1960 to 2009 (Gall et al., 2011). Flood waves generated from extreme precipitation events or infrastructure failure propagate from the origin along a channel network and are influenced by the geometric and physical properties of the channels along its path. Forecast centers simulate hydrologic processes using a framework of atmospheric and hydrologic models coupled with routing models to simulate flood wave propagation, and parameterization of channel properties within these models is necessary for forecasting of flood waves and thus the mitigation of potential damage. Sparse observational data availability renders the adequate characterization of channel properties a challenging task and typically requires some form of parameter regionalization. In this study, we seek to improve the flood simulation accuracy of the National Water Model (NWM) by replacing its current channel parameters with those based on a regionalization of an extensive observational database. This research is focused on the NWM channel routing module and therefore does not investigate parameterization of the land surface models (LSMs), the gridded routing module, or any other component of the NWM framework.

Agencies such as the National Oceanic and Atmospheric Administration (NOAA)
supply much of the actionable flood forecasting data for informed
policymaking and emergency management decisions. In many cases, these data
are produced by LSMs continuously forced by weather forecast data. This framework allows for the simulation of hydrologic processes occurring at individual watersheds forecast into the near future to produce actionable, time-sensitive hydrologic information. One emerging hydrologic modeling framework is the NOAA National Water Model (NWM). Launched in 2016, the NWM continuously simulates observed and forecast streamflow for approximately

The two-part routing system (gridded and NHD network based) employed by the
NWM represents a higher degree of sophistication compared to most other
mainstream operational models. For example, the Sacramento Soil Moisture
Accounting Model (SAC-SMA; Burnash et al., 1973) does not implicitly route flow between conceptual reservoirs, and the Hydrology
Laboratory–Research Distributed Hydrologic Model (HL-RDHM; Koren et al., 2004) assumes uniform, conceptual hillslopes within a relatively coarse

Additional observational data may enhance the representation of the routing
module, thereby improving flood forecasts. The hydraulic geometry (HyG)
dataset is a new, unpublished collection of approximately

While HyG may be a significant improvement over the current observational database used by the NWM, the utilization of HyG across CONUS requires the estimation of channel properties where observations are not available. This form of parameter transfer is often termed regionalization. Regionalization is defined here as the transfer of parameters estimated at observed spatial units to unobserved units under the assumption of hydrologic similarity. Largely due to the diversity of contexts in which regionalization techniques are typically applied, there is no consensus on which technique is best (Ayzel et al., 2017). A wide variety of regionalization techniques have historically been developed to make estimates at ungauged locations, though most may be broadly categorized into one of two main forms, i.e., distance based and regression based (He and Wilkerson, 2011; Livneh et al., 2013).

The first group of regionalization methods is based on distance, premised on the notion that parameters are continuously distributed through space, and the similarity between two arbitrary points is correlated with spatial proximity. The spatial structure of this correlation is modeled with varying types of interpolation, and the underlying statistical basis of these models varies widely. Typical regionalization methods which fall under this category include the method of inverse distance weighting (IDW), the nearest-neighbor (NN) method, and the method of Kriging, with the latter two generally considered as being the most widely used (Ayzel et al., 2017). For the specific application to the NWM channel network, grid-based spatial interpolations of channel parameters may be inapplicable. While one routing module in the NWM framework does route flow on a 250 m grid, the river network within the routing module of interest is not represented as a spatially continuous grid but rather a dendritic network of features overlaid on a spatially continuous land surface. In this case, two seemingly proximal channels may instead be distant from the perspective of the network and, consequently, have dissimilar properties due to natural variations in geology and terrain, vegetation, and development-related disturbances (e.g., urban drainage systems).

The second group of regionalization methods is not constrained by spatial
proximity and instead seeks to transfer parameters on the basis of similarity in physiographic features (land cover, soil, slope, etc.). Rather than spatial interpolation, similar catchment features can be found across long distances, such that the regionalization proceeds along dimensions of similar hydrologic features rather than distance. Regression-based approaches are examples of this category and are typically of a linear form (e.g., Gitau and Chaubey, 2010; Heuvelmans et al., 2006) although nonlinear, weighted, and sequential forms have also been applied (e.g., Abdulla and Lettenmaier, 1997; Kay et al., 2006; Li et al., 2010). Regional-scale regression curves for channel geometry, first developed by Dunne and Leopold (1978), operate on the assumption of similarity in geology, soil, climate, and hydrology within the region (Bieger et al., 2015). The current implementation of the NWM routing module parameterizes channel geometry through regression-based regional curves relating channel top width with the NHDPlus drainage area following the method of Blackburn-Lynch et al. (2017). Hydraulic roughness (Manning's

In this study, we hypothesize that enhancements in simulated streamflow goodness-of-fit (GOF) metrics performance are possible through an update to the NWM channel routing geometry and hydraulic roughness parameters. Therefore, the objectives are to (1) better characterize the influence of channel parameters on NWM-simulated streamflow, (2) develop a regionalization strategy for the HyG dataset such that a spatially complete and representative parameter dataset may be developed, and (3) examine the effects of this regionalized dataset on model flow GOF metrics performance. A greatly expanded database of channel geometry and hydraulic roughness regionalized to unobserved reaches may represent a substantial improvement to channel parameters in the NWM. Furthermore, assessing the degree of improvement attainable from updating channel routing parameters addresses a knowledge gap relevant to future model calibration efforts.

The analysis begins with a description of selected NWM channel parameters
and transformations where applicable (Sect. 2.2). A sensitivity analysis of
these channel parameters is then conducted to determine influence of channel
parameters on simulated streamflow (Sect. 2.3). Following this, channel
parameters are developed from HyG data at observed locations (Sect. 2.4) and
regionalized through multiscale regression-based approaches to all

Channels within the NWM routing module are represented by a compound
trapezoidal geometry (Fig. 1), consisting of a main channel that carries
baseflow and runoff up to bankfull flow conditions, and a conceptual
floodplain which carries overbank flow in times of flooding. For examination
of the sensitivity analysis, six parameters from the routing module that
describe the channel dimensions were selected, namely bottom width (BW), top width (TW), floodplain top width (TW

Cross-sectional diagram of the trapezoidal channel schematic used in the channel routing module of the NWM. This compound channel representation consists of a main channel (dark gray) and a floodplain (light gray) which becomes inundated in times of overbank flooding in the main channel. Parameters in blue were used to compute the parameters in orange for consistency among inputs for the sensitivity analysis. Parameters in black remained unchanged.

A sensitivity analysis was conducted to establish the influence of channel parameters on model streamflow output (Pianosi et al., 2016). To generate combinations of values within the parameter set, a Latin hypercube sampling (LHS) method was used to systematically sample across a hyperdimensional space. LHS is based on the Latin square design, which contains a single sample in each row and column of a hypothetical square with edges representing the ranges of two parameters (McKay et al., 1979). In this method, cumulative density functions (CDFs) for each parameter are divided into equal partitions, and data points within each partition are selected and randomly combined with other selected parameter values. LHS was chosen as it offers an advantage over random sampling techniques by ensuring representativeness of the real variability among the parameters of each randomly selected combination.

Given a lack of strict boundary conditions for the parameter values, inputs
were instead varied as a function of their nominal values developed from
regional curve relationships with drainage area (for estimating geometry
parameters), following Blackburn-Lynch et al. (2017) and the expert opinion scaled by Strahler stream order (for estimating Manning's

We employ the variance-based method of Sobol' (2001) for analysis of the NWM channel routing module parameter sensitivity, following the precedent set by many prior sensitivity analyses of hydrologic models (e.g., Abebe et al., 2010; Baroni and Tarantola, 2014; Cibin et al., 2010; Herman et al., 2013; Massmann and Holzmann, 2012; Nossent et al., 2011; Pappenberger et
al., 2008; Reusser et al., 2011; Song et al., 2012; Tang et al., 2007; Wagener et al., 2009; Yang, 2011; Zelelew and Alfredsen, 2013). Specifically, we follow the method of Saltelli (2002), using the sobolSalt function within the sensitivity R module (Iooss et al., 2021) to estimate the first-order (the influence of each parameter alone) and total effect (first order plus all interactive effects) indices, which implements a Monte Carlo estimation of the Sobol' indices at a cost of

A total of

Map of study domains, with red points showing locations for 12 representative basins dispersed across CONUS used for the channel routing module sensitivity analysis. These numbers correspond to the USGS gauge IDs listed in the table. Numbers and boundaries on the map correspond to the 18 designations and the extents of Hydrologic Unit Code (HUC)2 regions.

A collection of output metrics describing model fit to observed data, including normalized mean bias (NMB; Yu et al., 2006), Nash–Sutcliffe efficiency (NSE; Nash and Sutcliffe, 1970), and Richards–Baker flashiness index (R–B index; Baker et al., 2004), were used to reduce the model output time series to scalar values more readily comparable to the input parameter set. Equations for these metrics are provided below, as follows:

Channel parameters were first estimated at HyG-associated NHD reach segments and then subsequently estimated at all CONUS river reaches through a regression-based regionalization approach. The at-a-station hydraulic geometry of a channel (AHG) was calculated by relating the cross-sectional variation in stream discharge with width, depth, and velocity using power law relationships (Leopold and Maddock, 1953), as follows:

Manning's

For estimating the channel geometry parameters of BW and

We conducted an analysis of the regionalization method using the Manning's

Training of the regionalization regression equations for Manning's

To facilitate a standardized method for evaluating the regionalization, a

To understand the regional- and national-scale implications of new channel
parameters, the NWM routing module was run across the entirety of the

Summary of Manning's

The experimental trials were evaluated with the objective of identifying
whether errors affecting the GOF metrics performance were reduced relative to
the default configuration. This evaluative approach was used because the
routing module only controls the flow routing through the system rather
than total flow volume. We compared the hourly streamflow output of each
trial at observed reaches CONUS-wide, using available gauge observations, and
also conducted a closer examination of simulated flows for a selection of
individual gauges from the 12 representative basins (Fig. 2). For the
CONUS-wide analysis, GOF metrics such as percent bias (Eq. 3), NSE (Eq. 4), and

Across all calculated metrics and domains, Manning's

Sensitivity analysis results for the NWM channel routing module in 12 representative basins (Fig. 1). Estimated first-order indices are listed in panels

The regression fit between

Summaries of

CV results from the

A summary of median error in Manning's

Overall, nearly half of the HUC2 regions (8 of 18) showed the 99th percentile as the optimal flow percentile. However, the optimal regression fit was relatively balanced between the HUC2 and HUC4 regionalization scales, with eight regions minimizing the error at HUC2 scale and nine regions minimizing the error at the HUC4 scale. Variability in the error was highest in the lower Mississippi region (08), where the ratio between slope and Manning's

In comparison to the default parameterization, the experimental parameter
combinations described in Fig. 3 resulted in substantial differences to
both the estimated Manning's

Spatial maps illustrating default parameterizations, updated
parameterizations, and their percent differences across CONUS for Manning's

Across the 6841 USGS gauge locations with continuous information across the
experimental period, the median percent difference between default Manning's

Density plots of percent changes in cross-sectional area and
Manning's

Among the experimental trials, variance was generally low (approx.

Summary metrics at 4655 USGS gauge locations for the HUC4
regression scale and the TW99.9 combination experimental trial calculated across CONUS-wide gauge locations. Panel

Overall, mean

Of the 12 representative basins (Fig. 2), two gauges at outlets were selected for further examination based on the relatively high degree and opposing directions of change made to the parameterization of Manning's

Noticeable differences in the behavior across the experimental scenario results exist between the two selected gauges (Fig. 10). While NSE,

A summary of experimental results at two gauge locations. Panels

Results from the sensitivity analysis showed that channel roughness
(Manning's

Though the results were largely conclusive, several aspects of the sensitivity analysis may be modified in potential future studies. For
example, the selected boundary conditions ranged from 0.1 to 10 times the
nominal parameter values, which may not be reflective of the true uncertainty in these parameter values. The possibility also exists that parameter sensitivity is flow dependent, which may be most obvious in the case of the parameters TW

The regionalization of channel parameters was performed using a HUC-based
approach, where discrete regions were used to define the regression curves
used to estimate channel parameters within those regions. The principal
finding in comparing regionalization scales was that a smaller scale
typically results in the lowest error (e.g., Fig. 6), and the magnitude of
this difference is likely dependent on the inherent spatial variability in
the region in which the regressions were developed. For example, the
relatively poor performance of the full regression in the topographically
variable, mountainous HUC2 regions demonstrate the non-representativeness of
regressions developed using all measurements across CONUS for these unique
and topographically complex areas. Furthermore, the strong performance of
the HUC4 regionalization scale relative to HUC2 in the Missouri region (10)
speaks to the diversity of terrain conditions within this region, as it
encapsulates both mountainous terrain in the west and flatter plains in the
east. Overall, these findings underscore the importance of taking into account the spatial variability in the Manning's

The HUC-based discretization method, coupled with differences in observational data uncertainty and availability, naturally creates discontinuities at HUC boundaries in the regression parameters. Alternative regionalization approaches may help to alleviate or even remove the errors arising from these discontinuities; for example, a downstream hydraulic geometry (DHG)-based regionalization approach that takes into account observational data from nested gauges within the network to generate channel parameters along a flow path is one possibility that has seen previous success (Allen et al., 2018; Neal et al., 2015).

The estimation of regional regression curves for Manning's

With only a modest sensitivity of model output to channels parameters, results from both the sensitivity analysis and simulations demonstrate the limited influence of the channel routing module to improve GOF metrics within the overall NWM framework. In most cases, low variability in GOF metrics among trials is evident; though in some instances, such as at USGS gauge 09064600, there is some identifiable improvement from the default parameterization. Yet, even here, model hydrographs were unable to match observations. This is expected, as total volume is unaffected by the routing module, and thus the mass is conserved regardless of channel parameterization. However, in the course of model improvement, an appropriate philosophy is to do no harm, which largely characterizes the outcome of these experiments.

Parameters within the Noah-MP LSM not included in the sensitivity analysis or regionalization are likely the source of a large percentage of error, with meteorology and physics representations representing other potential sources. A previous sensitivity analysis conducted on the Noah-MP model indicated high sensitivities for output states and fluxes such as sensible and latent heat, soil moisture, and net ecosystem exchange derived from soil and vegetation parameters (Arsenault et al., 2018). Another showed sensitivity for latent heat and total runoff attributable to two-thirds of applicable standard parameters and the highest sensitivity derived from a hard-coded parameter value in the model used in the formulation of soil surface resistance for direct evaporation (Cuntz et al., 2016). Given these results, future efforts focused on the joint calibration of the Noah-MP LSM and channel routing module may result in noticeable GOF metrics improvements.

This analysis explored the effects of modifying channel routing parameters in the National Water Model streamflow simulations using a regionalized hydraulic geometry and Manning's

New estimates of NWM channel parameters following a regression-based regionalization approach generally results in a larger distribution of channel characteristics over the NWM v2.1 default parameterization. Overall,
variance in both Manning's

For Manning's

Channel geometry updates resulted in a longitudinal gradient in the percent change in the cross-sectional area. In the east, and particularly in the lower Mississippi region, the cross-sectional area increased, while a decrease in area is visible throughout smaller streams in the more arid west.

The influence of the routing module over modeled streamflow GOF metric performance is limited compared to other components of the NWM framework, such as the land surface model and meteorological input data. Future approaches towards the calibration of the NWM may yield the largest benefits through a more holistic approach to calibrating the overall framework, i.e., a comprehensive evaluation and calibration of all model components. Towards this objective, our characterization of the overall effects of strengthening channel routing module parameter representativeness may serve as an important foundation for the further improvement of the NWM and hydrologic modeling in CONUS. In turn, the NWM becomes better positioned to meet the stated goal of providing quality, actionable guidance for the mitigation of flood-related damages.

The underlying code and data are available upon request from the corresponding author.

AH conducted the evaluation and wrote the manuscript. BL provided advice and edited the manuscript. JM and LR provided model output data and served as points of contact for model operations. JK edited the manuscript. TM provided the dataset used in the evaluation and gave advice.

The contact author has declared that none of the authors has any competing interests.

Publisher’s note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

This research has been supported by the National Oceanic and Atmospheric Administration (grant no. NA18OAR4590391).

This paper was edited by Pieter van der Zaag and reviewed by two anonymous referees.

^{®}modeling system technical description, Version 5.1.1, NCAR Technical Note, 107 pp.,