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Resilient Design with Distributed Rainfall-Runoff Modeling (2023)

Chapter: Chapter 2 - Literature Review

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Suggested Citation:"Chapter 2 - Literature Review." National Academies of Sciences, Engineering, and Medicine. 2023. Resilient Design with Distributed Rainfall-Runoff Modeling. Washington, DC: The National Academies Press. doi: 10.17226/27051.
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Suggested Citation:"Chapter 2 - Literature Review." National Academies of Sciences, Engineering, and Medicine. 2023. Resilient Design with Distributed Rainfall-Runoff Modeling. Washington, DC: The National Academies Press. doi: 10.17226/27051.
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Suggested Citation:"Chapter 2 - Literature Review." National Academies of Sciences, Engineering, and Medicine. 2023. Resilient Design with Distributed Rainfall-Runoff Modeling. Washington, DC: The National Academies Press. doi: 10.17226/27051.
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Suggested Citation:"Chapter 2 - Literature Review." National Academies of Sciences, Engineering, and Medicine. 2023. Resilient Design with Distributed Rainfall-Runoff Modeling. Washington, DC: The National Academies Press. doi: 10.17226/27051.
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Suggested Citation:"Chapter 2 - Literature Review." National Academies of Sciences, Engineering, and Medicine. 2023. Resilient Design with Distributed Rainfall-Runoff Modeling. Washington, DC: The National Academies Press. doi: 10.17226/27051.
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Suggested Citation:"Chapter 2 - Literature Review." National Academies of Sciences, Engineering, and Medicine. 2023. Resilient Design with Distributed Rainfall-Runoff Modeling. Washington, DC: The National Academies Press. doi: 10.17226/27051.
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Suggested Citation:"Chapter 2 - Literature Review." National Academies of Sciences, Engineering, and Medicine. 2023. Resilient Design with Distributed Rainfall-Runoff Modeling. Washington, DC: The National Academies Press. doi: 10.17226/27051.
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Suggested Citation:"Chapter 2 - Literature Review." National Academies of Sciences, Engineering, and Medicine. 2023. Resilient Design with Distributed Rainfall-Runoff Modeling. Washington, DC: The National Academies Press. doi: 10.17226/27051.
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Suggested Citation:"Chapter 2 - Literature Review." National Academies of Sciences, Engineering, and Medicine. 2023. Resilient Design with Distributed Rainfall-Runoff Modeling. Washington, DC: The National Academies Press. doi: 10.17226/27051.
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Suggested Citation:"Chapter 2 - Literature Review." National Academies of Sciences, Engineering, and Medicine. 2023. Resilient Design with Distributed Rainfall-Runoff Modeling. Washington, DC: The National Academies Press. doi: 10.17226/27051.
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Suggested Citation:"Chapter 2 - Literature Review." National Academies of Sciences, Engineering, and Medicine. 2023. Resilient Design with Distributed Rainfall-Runoff Modeling. Washington, DC: The National Academies Press. doi: 10.17226/27051.
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Suggested Citation:"Chapter 2 - Literature Review." National Academies of Sciences, Engineering, and Medicine. 2023. Resilient Design with Distributed Rainfall-Runoff Modeling. Washington, DC: The National Academies Press. doi: 10.17226/27051.
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Suggested Citation:"Chapter 2 - Literature Review." National Academies of Sciences, Engineering, and Medicine. 2023. Resilient Design with Distributed Rainfall-Runoff Modeling. Washington, DC: The National Academies Press. doi: 10.17226/27051.
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Suggested Citation:"Chapter 2 - Literature Review." National Academies of Sciences, Engineering, and Medicine. 2023. Resilient Design with Distributed Rainfall-Runoff Modeling. Washington, DC: The National Academies Press. doi: 10.17226/27051.
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Suggested Citation:"Chapter 2 - Literature Review." National Academies of Sciences, Engineering, and Medicine. 2023. Resilient Design with Distributed Rainfall-Runoff Modeling. Washington, DC: The National Academies Press. doi: 10.17226/27051.
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Suggested Citation:"Chapter 2 - Literature Review." National Academies of Sciences, Engineering, and Medicine. 2023. Resilient Design with Distributed Rainfall-Runoff Modeling. Washington, DC: The National Academies Press. doi: 10.17226/27051.
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Suggested Citation:"Chapter 2 - Literature Review." National Academies of Sciences, Engineering, and Medicine. 2023. Resilient Design with Distributed Rainfall-Runoff Modeling. Washington, DC: The National Academies Press. doi: 10.17226/27051.
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Suggested Citation:"Chapter 2 - Literature Review." National Academies of Sciences, Engineering, and Medicine. 2023. Resilient Design with Distributed Rainfall-Runoff Modeling. Washington, DC: The National Academies Press. doi: 10.17226/27051.
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Suggested Citation:"Chapter 2 - Literature Review." National Academies of Sciences, Engineering, and Medicine. 2023. Resilient Design with Distributed Rainfall-Runoff Modeling. Washington, DC: The National Academies Press. doi: 10.17226/27051.
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Suggested Citation:"Chapter 2 - Literature Review." National Academies of Sciences, Engineering, and Medicine. 2023. Resilient Design with Distributed Rainfall-Runoff Modeling. Washington, DC: The National Academies Press. doi: 10.17226/27051.
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Suggested Citation:"Chapter 2 - Literature Review." National Academies of Sciences, Engineering, and Medicine. 2023. Resilient Design with Distributed Rainfall-Runoff Modeling. Washington, DC: The National Academies Press. doi: 10.17226/27051.
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Suggested Citation:"Chapter 2 - Literature Review." National Academies of Sciences, Engineering, and Medicine. 2023. Resilient Design with Distributed Rainfall-Runoff Modeling. Washington, DC: The National Academies Press. doi: 10.17226/27051.
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8 Background of Hydrological Modeling and DRRMs Hydrological modeling is an integral part of civil engineering practice. Giere (2004, p. 747) stated that “models represent aspects of the world for specific purposes.” And in the case of hydrological models (HMs) and transportation infrastructure, engineers use HMs to represent aspects of the hydrological cycle that have short- or long-term impacts on such infrastructure. Aligned with the purpose of a given modeling effort, the extent of the hydrological cycle represented by each HM tool varies, and thus its usefulness and capabilities do too. One of the most important uses of hydrological modeling is the ability to safely anticipate peak flow rates that need to be conveyed by drainage structures such as channels and culverts. For hundreds of years, engineers and scientists observed that certain rain events, albeit infrequent, could overwhelm existing drainage features and create destructive flooding, with impacts to public health and safety and the economy. They also observed that these impacts were affected by factors that are now well understood, such as infiltration, evaporation, soil characteristics, and land use, among others. Dooge (1974) alluded to the pioneering work by Mulvaney (1851) who set the basis to the current Rational Method, which was popularized in the United States by Kuichling (1889). The Rational Method was conceived to estimate peak flow rates and is ideally used in applications involving smaller sub-catchments with relatively uniform land use and soil types. Developments and improvements on the Rational Method took place over the years, including adjustments to the runoff coefficient C (Westphal 2001; Thompson 2006; Dhakal et al. 2012; Dhakal et al. 2013a; Dhakal et al. 2013b). Other developments included the derivations of hydrographs based on the assumption that flow rates increase linearly with time until the time of concentration is reached, and the entire sub-catchment contributes toward the peak flow (Poertner 1974; Dhakal et al. 2014). An alternative to the Rational Method for determining peak flows in urban and undevel- oped sub-catchments is regression equations. Regression equations have been developed by the U.S. Geological Survey (USGS) and other agencies across the globe through least square regression procedures that use independent variables to characterize various features, including peak flows. One tool that conveniently enables regression equation method results for various states across the United States is the web platform StreamStats (https://streamstats.usgs.gov/ss/) (Curran et al. 2016). However, as Westphal (2001) points out, hydrological design based on peak flow methods is not appropriate in several practical conditions. The author pointed to the difficulties in obtaining peak flow estimates in larger watersheds, with a longer time of concentration, and great non- uniformity in rainfall, land use, and soil characteristics. Another factor preventing a successful use of peak flow methods is when watersheds have lakes/reservoirs or other types of water storage, which influences the drainage time and runoff outflows. C H A P T E R   2 Literature Review

Literature Review 9 In such cases, the runoff hydrograph is needed to achieve an adequate design of drainage struc- tures rather than a peak flow. A wider range of hydrologic processes needs to be represented in such models to derive outflow hydrographs, including the following: • Rainfall estimates over time, which are often assumed to be uniform over the watershed area but might vary over time. One example often used is synthetic hyetographs with triangular shapes (Asquith et al. 2003; Hawkins et al. 2017). • Rainfall abstractions (or rainfall losses) estimates that consider soil characteristics, initial soil moisture conditions, land use type, tree canopy interception, depression storage, and other related abstractions (Chow et al. 1988). • Procedures to derive outflow hydrographs for watersheds, which can be classified into two main groups: (1) UH-based methods and (2) physically based methods. These methods are further discussed in the next paragraph. • Route hydrographs through streams/rivers and lakes/reservoirs using hydrologic routing methods—for example, Muskingum routing method, linear or nonlinear reservoir routing methods (Chow et al. 1988)—and physically based routing methods such as solving the shallow-water flow equations (Chaudhry 2008). UH methods use mathematical procedures, such as convolution, to transform the excess rain- fall into a direct runoff hydrograph, which becomes a streamflow hydrograph after adding the base flow from the groundwater flow release (Chow et al. 1988). Examples of methods using the UH approach include the Snyder (1938) method and the SCS dimensionless UH method (Cronshey et al. 1986). Computer models that implement UH methods include the Windows WinTR-20 (Hawkins et al. 2017), WinTR-55 (NRCS 2009), HEC-HMS (Feldman 2000), and other hydrological models. Physically based methods, by contrast, use conservation laws at distinct compartments of the hydrological cycle (Julien and Saghafian 1991), keeping track of the runoff flow, infiltration losses, evaporation, and so forth, as runoff moves through the watershed. By tracking the flow compo- nents through space and time, physically based models may attain both event-based (i.e., single rainfall) or continuous (i.e., over multiple rain events) hydrological simulations. Physically based methods can possibly improve peak flow calculation (Refsgaard et al. 2010), allowing for hydro- graph computation and, in certain cases when the formulation allows, contaminant tracking in watersheds (Downer and Johnson 2011). Beyond design goals, physically based models can help with the real-time management of watersheds, environmental assessments such as aquatic species mobility, and consideration of long-term effects, such as climate change. The majority of DRRMs are built using physically based formulations and differ in how they represent the different components of the hydrological pro- cess. The next section discusses DRRMs in more detail and presents the differences in the formu- lation used in some of these models. Types of DRRMs and Key Model Components The hydrological cycle in a watershed has many interconnected components or processes, and the computation of the runoff at the watershed outlet is a common task for engineering design. The runoff prediction for engineering practice has a long history. Early hydrologists/engineers calculated peak discharge of surface runoff using limited data and simple computational tech- niques. Contemporary runoff modeling techniques start with rainfall as input and consider various intermediate hydrological processes with more complex computational procedures. The rainfall-runoff models can be classified in many ways, as not all models fit into a single category because they are developed for various purposes (Woolhiser 1973).

10 Resilient Design with Distributed Rainfall-Runoff Modeling Based on a model’s structure (i.e., how runoff is calculated), Sitterson et al. (2017) classified the rainfall-runoff models as empirical, conceptual, and physical. Empirical models use non- linear relationship between inputs and outputs and are also called “black box models.” Concep- tual models use simplified equations to represent water balance/storage in catchment. Physical mechanistic models use physical laws and equations based on real hydrologic responses (Julien and Saghafian 1991; Sitterson et al. 2017). To present the spatial processes in a catchment for rainfall-runoff modeling, Sitterson et al. (2017) classified the rainfall-runoff models as lumped, semi-distributed, and distributed (i.e., using grid cells) models. Lumped models predict the runoff for a single homogenous catchment. Empirical or regression models and some conceptual models are examples of lumped rainfall-runoff models. In this synthesis, the DRRMs include the semi- distributed models using sub-watersheds/-catchments and distributed models by grid cells. DRRMs can be derived from physically based mathematical models—for example, from phys- ical hydrology (Freeze and Harlan 1969)—and/or other semi-empirically based approaches. The key distinction between lumped models and DRRMs is that DRRMs do not treat watersheds as a “black box,” but rather each relevant component of the hydrological process is represented through or approximated by mathematical expressions for these natural processes. Moreover, the spatial heterogeneity within the area of interest in any modeling study is explicitly accounted for (hence the term “distributed”) through smaller spatial units. These spatial units are created to group areas with similar characteristics, such as land use, soil properties, and water features (e.g., streams and lakes). The process of performing the subdivision of a watershed is often referred to as “discretization” (Wang et al. 2016; Moore et al. 2017), and DRRMs typically perform the discretization using the following two main approaches: • Gridded-based division: The watershed is represented through sub-areas created through grids regularly distributed in space. The area within each grid is small enough to assume relevant hydrological parameters to be homogeneous. An example of an implementation of a gridded- based DRRM is presented in Figure 2, focusing on the computation of sediment transport in a watershed. • Sub-catchment-based division: Sub-watersheds are delineated with the help of a DEM, and these represent the spatial heterogeneity in the study area. Certain sources (Sitterson et al. 2017) classify models using sub-catchment-based divisions as semi-distributed models (see Figure 1), but in this synthesis these models are referred to as “distributed” along with gridded models. Beyond the catchment itself, other criteria for further subdivision might include land use and soil characteristics. An example of an implementation of a sub-catchment-based DRRM is presented in Figure 3, with focus on estimating peak flow. In this work, Moore et al. (2017) evaluated changes in the stream hydrology and water quality created by I-59N using a calibrated semi-distributed model. The formulation of DRRMs needs to consider various elements that represent key components of the hydrological cycle. According to Ivanov et al. (2004) and Rossman and Huber (2016), DRRMs often include modeling components that represent the following: • Meteorological data to express the interactions of watersheds with the atmosphere over time that include rainfall hyetographs, snowfall amounts, wind speeds, and temperature. • Rainfall abstraction or losses are represented through time-varying infiltration formulae, canopy interception, evapotranspiration, and depression storage, among others. • Runoff generation and routing represent the motion of surface water that comprises the excess runoff. These include the overland runoff routing (e.g., sheet flows) and hydraulic routing schemes to represent flows in streams and water bodies with larger depth. • Groundwater is represented by applying conservation laws expressing mass and energy, having interactions with the surface water, including infiltration and exfiltration.

Literature Review 11 Figure 2. Implementation of a gridded DRRM with a focus on estimating erosion and deposition from hydrological modeling results (Downer and Johnson 2011). Figure 3. Implementation of a sub-catchment-based DRRM with a focus of estimating peak flows along a stream crossing with I-59N near Trussville, AL (Moore et al. 2017).

12 Resilient Design with Distributed Rainfall-Runoff Modeling • Although not directly related to hydrological processes, DRRMs can, in certain cases, include features that enable the tracking of constituents and pollutants in the water. As indicated, DRRMs have a variety of components that enable physics-based approaches to represent the hydrological behavior of watersheds. Although data requirements for the opera- tion of DRRMs are comparatively higher than lumped hydrological modeling tools, Geographic Information System (GIS) databases can significantly facilitate the implementation of DRRMs. The capabilities and advantages of DRRMs are discussed in the next section. Advantages of DRRMs over Lumped Approaches Surface hydrological systems connect the atmosphere, natural streams, constructed convey- ances, natural and artificial reservoirs, shallow aquifers, and ecosystems. For decades, hydrolo- gists described these complex systems using simplifying approaches that lumped the spatial variability and the physical processes in fewer parameters. Lumped hydrological modeling approaches include the following (Sitterson et al. 2017): • Rational Method and the modified Rational Method; • Regression equations, which are Regionalization Methods in which watershed parameters are transferred to similar catchments (Blöschl and Sivapalan 1995) that enable estimates of peak and low flows; and • Statistical methods [i.e., flood frequency analysis (FFA)] to estimate peak flows. These methods have become popular in transportation agencies due to their relative simplicity and ability to provide rapid assessments for hydrological design in transportation projects. The fundamental components of lumped hydrological modeling are presented in Figure 4. Although the advantages and shortcomings of these lumped hydrological modeling approaches were briefly presented in the section “Background of Hydrological Modeling and DRRMs” earlier in this chapter, they are discussed in more detail in this section. Although simple to apply, lumped approaches rely on various assumptions such as the unifor- mity of watersheds and intrinsic limitations and assumptions that can over- and underestimate runoff values (Sitterson et al. 2017). Those include the following: Figure 4. Fundamental components of lumped hydrological modeling that average spatiotemporal characteristics of watersheds. Based on Downer and Johnson (2011).

Literature Review 13 • Most applications of lumped approaches are event based, and the predictions are related to a design rain event of a specific return period or duration (COMET 2006). However, the time scale associated with certain hydrological processes (e.g., floods) is often distinct from the typical duration of individual rain events, as other components of the local hydrology (e.g., groundwater) interact with streams (Moore et al. 2017). • Processes such as rainfall and infiltration are complex and time varying (Abbott et al. 1986), and most lumped approaches do not enable adjustment of rainfall loss and result in inaccuracies. • Spatial heterogeneity is also simplified in lumped approaches, and detailed spatial features are neglected (COMET 2006). The approach of spatially averaging parameters (such as run off coefficients) over larger areas creates uncertainties, affecting modeling accuracy. Neglecting spatial features will also simplify the representation of flow paths, influencing the timing of a watershed response to rain events and corresponding abstractions (Downer and Johnson 2011). In all, the accuracy limitations lead to uncertainties that result in difficult decision making aimed at improving transportation resiliency (Lago et al. 2021). The extent of calculations and data requirements needed to overcome these shortcomings is such that computer-based modeling tools become necessary. DRRMs are implemented in different commercial and open-source tools that have undergone development for many years. The potential advantages that DRRMs have over lumped approaches include the following: • DRRMs have the potential of yielding more realistic water balance calculations in watersheds (Abbott et al. 1986). DRRMs have various hydrological compartments in which water volumes are tracked, such as streams, surface reservoirs, and shallow-water aquifers. The models also have equations describing the exchange between these compartments, such as the exfiltration of groundwater into streams or the infiltration of rainfall into the unsaturated soil. • Certain assumptions, such as the directions of flow paths, are not needed by grid-based DRRMs (Figures 1 and 2) to describe overland flows. Because of the increased spatial dis- cretization, each overland flow path component is calculated independently using physically based expressions (Julien and Saghafian 1991). • Because DRRMs can perform extended-period analysis, the effect of previous conditions (e.g., recent rainfall) can be explicitly accounted for in calculations (Rossman and Huber 2016). This enables, for instance, infiltration to become less relevant for long rain events or conditions involving multiple rain events. • The integration of DRRMs with various electronic data sources (e.g., rainfall data, land cover data, soil properties) facilitates the development of various what-if scenarios compared with lumped approaches with less automatized calculations. • DRRM outputs can be coupled with geospatial tools, which in turn can facilitate the com- munication of results with a wider audience. For instance, flooding extents and animations of flooding episodes can be computed with DRRMs (Brunner 2016), which in turn helps high- light the impacts of such extreme events. Representative DRRMs with a Brief Model Description The DRRMs presented in this section have been created by several parties, some with a devel- opment that spans multiple decades. Organizations that have developed DRRMs include the following: • U.S. Army Corps of Engineers (USACE), through HEC (HEC-HMS and HEC-RAS) and Coastal and Hydraulics Laboratory (CHL) [Gridded Surface Subsurface Hydrologic Analysis (GSSHA)]; • U.S. Environmental Protection Agency (EPA), through the National Risk Management Research Laboratory (SWMM 5);

14 Resilient Design with Distributed Rainfall-Runoff Modeling • U.S. Bureau of Reclamation (USBR) [Sedimentation and River Hydraulics—Watershed (SRH-W)] (Lai et al. 2022); and • Private software companies. Although each DRRM has unique characteristics and features, there are important common- alities such as the following: • The representation of multiple hydrological compartments and the water fluxes between these. A contrast point between the tools is the extent to which the interactions between these compartments are represented. • A strategy for spatial discretization, whether based on splitting the watershed in smaller sub- catchments of sub-basins or using a gridded representation of rainfall, abstractions, overland flows, groundwater, and so forth. • Algorithms for channel routing, ranging from hydrological routings based on mass balance and storage relations, simplified versions of the one-dimensional (1-D) Saint-Venant equations (SVEs) (Sturm 2010), up to a full implementation of the two-dimensional (2-D) shallow-water equations (SWEs) (Chaudhry 2008). • An adequate treatment for natural or artificial reservoirs that are present in the watershed, which will create impacts in the response time of rain events. • The ability to perform both event-based simulations of a design or a synthetic rain event and continuous simulation scenarios. • A graphical user interface for pre- and post-processing to facilitate data input and result analysis. These interfaces often include geospatial tools or the ability to connect with geodatabases. A non-exhaustive list of DRRMs is presented in this section along with a brief discussion of these main characteristics and features. Most of these models are freely available to the public, as detailed in the subsections that follow. HEC-HMS The HEC developed the HMS in the early 1990s as a replacement for the earlier MS-DOS version HEC-1 model. The model performs a spatial discretization of a watershed through basin and sub-basin models, which corresponds to sub-catchments in the watershed. Sub- basins generate outflows that are routed by a dendritic network of reaches and reservoirs toward the outlet. HMS has a comprehensive suite of calculation modules, and model features include the following: • Meteorological models, including gridded or synthetic precipitation, evaporation, and so forth. • An assortment of different methods available to simulate rainfall losses, including four gridded abstraction methods (e.g., using the area’s CN). • Transformation of excess rainfall into surface runoff using UH methods. It also includes the kinematic wave method with multiple planes and channels for excess rainfall transformation. • Flow routing methods, such as hydrological routing or kinematic wave equation. • Groundwater interactions with streams is performed through a loss/gain equation. HEC-HMS has undergone various improvements over HEC-1, which include the integration of radar rainfall data; the use of GIS; and the ability of running continuous simulations, includ- ing evapotranspiration, snowmelt, and soil moisture accounting. In the most recent version, HEC-HMS 4.10, advanced capabilities are also provided for gridded runoff simulation using the linear quasi-distributed runoff transform [modified Clark (ModClark)]. HEC-HMS is widely applied by hydrologists in the United States, including in the context of roadway transportation design. The model is available for download, and an example of the user interface is presented in Figure 5.

Literature Review 15 GSSHA by the USACE GSSHA is a physically based model developed by the USACE through the CHL, which is a part of the Engineering Research and Development Center (ERDC). It includes a 2-D overland flow algo- rithm over a regular grid, and it has the ability to perform event-based or continuous simulations. A distinction between GSSHA and HEC-HMS is that the former uses a grid as the fundamental unit for calculation. Overland flows, infiltration and groundwater modeling, among other pro- cesses, are computed at each grid. GSSHA can simulate processes that have dissimilar time scales efficiently, tracking the water fluxes between hydrological components. The range of processes in the GSSHA formulation include the following: • Precipitation distribution in time and space and snowfall accumulation; • Abstractions that include interception, overland soil retention, and infiltration; Figure 5. Example of the graphical user interface of the HEC-HMS model (HEC 2022a).

16 Resilient Design with Distributed Rainfall-Runoff Modeling • Overland 2-D flow routing and channel routing; • Reservoirs/lake storage; • Vadose zone moisture and 2-D averaged lateral groundwater flow; and • Surface water/groundwater interaction and exfiltration. Although GSSHA is publicly available, it does not have a graphic user interface as do other models presented in this synthesis. The Watershed Modeling System (WMS) (AQUAVEO 2022) framework (Figure 6) provides a pre- and post-processor interface, and data can be supplied through integration with various data sources. WMS is freely available to state DOTs. HEC-RAS 2D by the USACE A hydraulic modeling tool developed by the USACE HEC is the River Analysis System, also known as HEC-RAS or RAS. It replaced the earlier MS-DOS version HEC-2 model and was initially conceived as a 1-D river modeling tool. Up to version 4, HEC-RAS simulated backwater effects, mixed (i.e., trans-critical) flow regimes, and sediment transport, among other capabilities. With the appearance of the initial versions of RAS 5.0 in 2015–2016, gridded 2-D simulation became possible, including overland flows simulation with the addition of rain over grid. This rain over grid is represented via a “Precipitation” boundary condition and corresponded to a time- varying, spatially uniform rainfall over the project area. The Precipitation boundary condition did not account for abstractions; thus, the effective rainfall should be calculated outside of the RAS model. The current version of this model (HEC-RAS 6.1) can represent time and spatially varying precipitation, wind, and infiltration. Some spatially variable data for RAS simulations are handled using the HEC-RAS Mapper tool, as shown in Figure 7. Although not conceived as a hydrological model, HEC-RAS has the ability to perform event- based or continuous simulations of overland flows created by variable rainfall that consider infil- tration. One aspect of the model that distinguishes it from GSSHA is that RAS has the SWEs built to simulate overland flows, whereas GSSHA performs this simulation using the diffusion wave equation. Also, unlike GSSHA, the current RAS version does not simulate groundwater. Similar to HEC-HMS, HEC-RAS is publicly available for download. Figure 6. Modeling results of overland and channel flows from a GSSHA simulation (ERDC 2012).

Literature Review 17 Storm Water Management Model by the U.S. EPA The Storm Water Management Model (SWMM) is a hydrologic–hydraulic modeling tool devel- oped by the U.S. EPA. With its origins going back to the early 1970s, SWMM has been one of the most used modeling tools in hydrologic simulation in urban areas. Over time, its applications have expanded to represent water quality modeling in catchments hydrology of undeveloped watersheds, both in terms of event-based and continuous simulations. Another feature added to SWMM since its version 5.1 is the ability to represent the effect of various Low-Impact Devel- opment (LID) controls to mitigate the impacts of peak flows and contaminants in the runoff. SWMM enables watershed representation via sub-catchments, similar to HEC-HMS, as illustrated in Figure 8. SWMM code is open source, and various software vendors and research groups have devel- oped tools and interfaces that use SWMM’s calculation engine. Particularly, private software vendors have enabled an integration of geospatial databases and SWMM to facilitate data entry (e.g., DEM, soil types, water bodies), calibration, and results presentation. In recent years, these pre- and post-processing tools also enabled the simulation of 2-D overland flows in a gridded fashion, similar to GSSHA and HEC-RAS. However, unlike GSSHA, the representation of ground- water flows is not gridded but rather based on discrete aquifer elements. The model continues its development, and anticipated improvements include a hydraulic engine that will enable more efficient use of multicore processing for large simulation tasks. SWMM is publicly available for download, and the source code is also publicly available. Figure 7. Point Precipitation with the Thiessen Polygon Interpolation Method yielded by HEC-RAS Mapper (HEC 2022b).

18 Resilient Design with Distributed Rainfall-Runoff Modeling SRH-2D by the U.S. Bureau of Reclamation At the time of the development of this synthesis, there is a new DRRM tool undergoing devel- opment by the U.S. Bureau of Reclamation (USBR). This model, SRH—two dimensions (SRH-2D), will add a hydrologic module (SRH-W) with runoff generation and soil erosion modeling capabilities (Lai et al. 2022). The model is being developed through a joint effort between USBR and the Taiwan Water Resources Agency. The model is designed to represent the hydrology of watersheds as small as 10 km2 and larger, and it should be applied with software that will help in the preparation of a gridded (Cartesian or unstructured) mesh. SRH-2D integrates various calculation modules, including meteorological, evaporation, sub- surface flow, and an optional 1-D channel network flow solver. Rainfall data can be radar based and gridded, using a piecewise constant interpolation to determine the precipitation at each 2-D Figure 8. SWMM of a watershed in Jefferson County, AL, north from U.S. Route 11 (Vasconcelos and Pachaly 2021).

Literature Review 19 mesh cell that represents the watershed. Overland flow is represented either by the 2-D zero- inertia equations (a.k.a. diffusion wave) and optionally by the 1-D channel network solver that uses SVEs. A demonstration of the application of the SRH-2D model is presented in the report by Lai et al. (2022) for a watershed in Iowa (see Figure 9). Unlike other DRRM tools, this model also has the capability of estimating soil erosion and sediment routing. The current estimate is that the SRH-2D will be available early in 2023. Table 1 summarizes some of the capabilities of the models that were presented in this section. Distributed Rainfall-Runoff Modeling Tools by Private Software Vendors A key aspect in the development and improvements of DRRMs has been privately owned software companies’ contributions. These contributions involve the development of pre- and Figure 9. Implementation of a computational grid in SRH-2D for Clear Creek Watershed, IA, and corresponding rainfall data grid (Lai et al. 2022). Model Name Spatial Discretization Overland Flow Routing Channel Routing Groundwater Interaction HEC-HMS Sub-catchments division Empirical UH models, kinematic wave Various hydrological routing, kinematic wave Included HEC-RAS 2D Gridded-based division Zero-inertia wave, SWE Zero-inertia wave, SWE Not included GSSHA Gridded-based division Manning-based or zero- inertia wave Manning-based or zero- inertia wave Included, gridded SWMM Sub-catchments division Nonlinear reservoir routing Kinematic wave and SVE Included SRH-2D Gridded-based division Zero-inertia wave SVE and SWE Included Table 1. Summary of the capabilities of DRRM tools presented in this synthesis.

20 Resilient Design with Distributed Rainfall-Runoff Modeling post-processing tools and the implementation of algorithms to represent relevant hydrological processes. These commercial tools have user interfaces that facilitate data entry and undergo frequent improvements and are supported by technical staff in these companies. State Agency Hydrologic Design Manuals State DOTs have been using hydrological tools for years and, in certain cases, DRRM tools have been adopted for hydrological studies. Through a search into each state DOT website, the hydrologic– hydraulic design manuals produced by each state agency were retrieved. The available information on hydrological modeling tools and DRRMs was compiled from these manuals. Table 2 presents the summary of the state agency practices on hydrological models, some of those lumped approaches traditionally adopted, and DRRM tools that are cited in published design manuals. Other State and Federal Studies Applying DRRMs In addition to design manuals or guidelines, DRRMs have been applied in various studies and evaluations by state DOTs, universities, and federal organizations. A literature survey using the term “hydrologic model” was performed using the NTL over a 20-year period (2001–2021), and the refer- ences that make direct reference or application of DRRMs were selected. The selected studies and reports that applied DRRMs in the context of highway infrastructure are listed in Table 3. Although the goals of these reports are unique, the studies can be classified in the following three broad types: • Applications of DRRMs to assess the vulnerability or the resiliency of transportation infrastruc- ture, including roads and bridges, to flooding events. Some of these studies have considered future climate change and sea-level rise in the hydrologic assessments. Those studies varied considerably in geographic scale, from selected watersheds to entire states, often incorporating the interactions between surface hydrology and groundwater. • Applications of DRRMs in conjunction with hydraulic models to evaluate processes such as bridge scouring, streambed mobility, sediment mobilization in watersheds, and sediment aggradation in in-stream structures. In those studies, the hydrological models provide inflow data that are subsequently used in hydrodynamic models that describe flow details near the in-stream structures. • Applications of DRRMs to evaluate the impact of stormwater runoff from roadways in terms of peak flows and water quality to receiving water bodies. Those studies often include field investi- gations, contaminant characterization, stormwater management practices, and hydraulic model- ing efforts. The DRRM is often applied to describe the rainfall-runoff transformation, but in some instances they were used to represent stormwater hydraulics and water quality modeling. Summary of the Literature Review The literature reviews on DRRMs have indicated the wide range of applications in which these tools are used in the context of transportation infrastructure and roadways. Historically, hydro- logic modeling in roadway applications involved lumped, semi-empirical approaches aimed at providing estimates of peak flows for the design of in-stream structures. These methods included gage data analysis, statistical regression, and the Rational Method. Over time, semi-empirical approaches such as the Natural Resources Conservation Service (NRCS) TR-20 and TR-55 enabled the computation of storm runoff volume and hydrographs for single events. DRRMs have benefited from various improvements on data gathering, model formulation, calibration techniques, and computational resources, among others, resulting in an expansion of the scope of studies involving hydrologic modeling. Application of DRRMs coupled with hydraulic

Literature Review 21 State Agency Hydrological Modeling Tools and DRRMs Adopted Sources Excerpts and Comments Alabama Department of Transportation Regression equations, Rational Method, WinTR-20, HEC-HMS, GSSHA ALDOT (2018) “If a higher degree of accuracy is warranted, or if the watershed is large and complex, use computer programs such as NRCS Technical Release 20 (TR-20), the USACE Hydrologic Engineering Center Hydraulic Modeling Software (HEC- HMS), USACE Gridded Surface Subsurface Hydrologic Analysis (GSSHA) model with AQUAVEO’s Watershed Modeling System (WMS).” Alaska Department of Transportation Regression equations, Rational Method, HEC-1 DOT&PF (1995) “US Army Corps of Engineers HEC-1 Flood Hydrograph package can be used if it can be calibrated and verified with actual rainfall and runoff data.” Arizona Department of Transportation Regression equations, Rational Method, HEC-HMS, FLO-2D ADOT (2014) “The rainfall-runoff modeling guidance is structured to be compatible with the US Army Corps of Engineers’ HEC-HMS Flood Hydrology program, as well as the FLO-2D two- dimensional flow model by FLO-2D Software, Inc.” Arkansas Department of Transportation Regression equations, Rational Method, TR-55 AHTD (1982) “Rainfall information for use in the Rational Method and TR-55 Method should come from the NOAA Atlas 14 data set available at the NOAA website.” California Department of Transportation Regression equations, Rational Method, HEC-HMS, TR-55, WMS- based models, Autodesk Civil three dimensional (3-D)/Hydraflow Caltrans (2018) “Most simulation models require a significant amount of input data that must be carefully examined by a competent and experienced user with an understanding of the mathematical nuances of the model and the hydrologic nuances of the particular catchment to assure reliable results. See Table 808.1 for hydrologic software packages that have been reviewed and deemed compatible with Departmental procedures.” Colorado Department of Transportation Regression equations, Rational Method, HEC-HMS, WinTR-20, WinTR-55, WMS-based models Gross et al. (2019) “The primary software for estimating peak discharge for ungaged streams is the USGS National Streamflow Statistics (NSS) software (see Table 7-8). Similar software based on the National Flood Frequency (NFF) is also available in the Watershed Management System (WMS) software. If a hydrograph is needed, WMS can be used to generate a hydrograph using the HEC-HMS, TR-20/TR-55, or a variety of other procedures.” Connecticut Department of Transportation Regression equations, Rational Method, HEC-1, HEC-HMS, TR-20, TR-55 CTDOT (2001) “In some cases, there may be a lag time between the storm surge discharge and the stream flow discharge at the highway crossing. For this case, stream flow-routing methods such as the NRCS TR-20, USACE HEC-1 or HEC-HMS model can be used to estimate the timing of the flood hydrograph derived from runoff of the watershed(s) draining into the sound or estuary.” Delaware Department of Transportation Regression equations, Rational Method, models referenced through FHWA Hydrologic Design Series (HDS) No. 2 manual McCuen et al. (2002) “Guidelines include DGMs on Personnel Safety Grates and a Sample Drainage Report. Manuals include Design of Urban Drainage, and HDS and HEC Manuals.” Florida Department of Transportation Regression equations, Rational Method, National Resources Conservation Service (NRCS) Unit Hydrograph (UH) methods FDOT (2022) “In general, you can apply procedures using streamflow analysis and unit hydrograph theory to all watershed categories. Table 2.2-1 shows guidelines for selecting peak runoff rate and flood hydrograph procedures.” Georgia Department of Transportation Regression equations, Rational Method, HEC-HMS, WinTR-20, WinTR-55, WMS-based models GDOT (2020) “If a higher degree of accuracy is warranted, or if the watershed is large and complex, use computer programs such as NRCS Technical release 20 (TR-20), the USACE Hydrologic Engineering Center Hydraulic Modeling Software (HEC- HMS), or AQUAVEO Watershed Modeling system (WMS).” Hawaii Department of Transportation Regression equations, Rational Method, NRCS-based methods HIDOT (2007) “This method is used for large watersheds where gage data are not available. However, the curve numbers, antecedent moisture content factors, and time of concentration curves shall be applicable to the site under consideration.” Table 2. State transportation agency hydrologic design manuals and guidelines. (continued on next page)

22 Resilient Design with Distributed Rainfall-Runoff Modeling Idaho Transportation Department Regression equations, Rational Method, HEC-HMS ITD (2021) “The program HEC-HMS, developed and maintained by the USACE Hydrologic Engineering Center, is a public-domain tool that can be used to perform rainfall-runoff analysis using a variety of methods.” Illinois Department of Transportation Regression equations, Rational Method, HEC-HMS, HEC-1, TR-20, WinTR-20 IDOT (2011) “State the method used to determine the discharges in the hydraulic model. Examples may include the StreamStats, stream gage data, HEC-1, HEC-HMS, TR-20, Win TR-20, or any other approved method.” Indiana Department of Transportation Regression equations, Rational Method, HEC-HMS, TR-20 INDOT (2014) “NRCS Unit Hydrograph Method TR-20 can be most often used to determine peak discharge and hydrograph for a given drainage basin size. However, the results have less confidence in a very flat drainage basin with potential watershed storage, or a very large drainage basin. This method is also used for design of a detention/retention pond or storage facility. HEC- HMS. This hydrograph method can be used under the same conditions shown above for TR-20.” State Agency Hydrological Modeling Tools and DRRMs Adopted Sources Excerpts and Comments Iowa Department of Transportation Regression equations, Rational Method, Bentley GEOPAK Drainage, models through FHWA HEC-22 manual IowaDOT (2015) “For most roadway stormwater drainage systems, the Rational Method can be used to determine peak flow (Q). If drainage areas involve pump stations or include topography or structures that retain or detain water, the Rational Method cannot be used. Use other nationally accepted methods… For drainage areas larger than 160 acres, other methods of determining peak flow [for example, the SCS (NCRS) peak flow method] are required. These are discussed in HEC-22.” Kansas Department of Transportation Regression equations, Rational Method, TR-55, TR-20 Young (2016) “It is noted that peak flows associated with hydrograph derivation may not agree with peak flows computed by regression methods or other methods based on instantaneous peak flow calculations. For design purposes, it is suggested that more than one method of hydrograph be used to aid the designer in judging the final results. As an alternative, the peak flow of the hydrograph may be adjusted to match the peak flow selected for the design discharge.” Kentucky Transportation Cabinet Regression equations, Rational Method, WinTR-55, WinTR-20, Hydrain-Hydro Module, WMS- based models KYTC (2010) “A consideration of peak flow rates for design is generally adequate for conveyance systems (e.g., storm drains or open channels). However, if the design must include flood routing (e.g., detention basins or complex conveyance networks), a flood hydrograph is usually required. Development of runoff hydrographs is usually accomplished using computer programs or tabular methods. Where storage is a significant factor and the drainage basin can be divided into homogeneous sub basins, hydrograph methods should provide better flow estimates.“ Louisiana Department of Transportation and Development Regression equations, Rational Method, Models referenced through FHWA HDS No. 2 manual LaDOTD (2011) “The methods for determining the peak discharge from gage data are described in the FHWA publication HDS-2 – Highway Hydrology. It is available on the FHWA website.” Maine Department of Transportation Regression equations and/or Rational Method for watersheds smaller than 320 acres MaineDEP (2016) “Results of hydrologic analysis and culvert sizing should always be considered in the context of the existing culvert size, performance and experience. For hydrology methods, consider areas of development, recently built or soon to be built, to understand how new flow may impact the roadway. Changes in land use can have a large impact on calculated peak flow. This can include changes from forest to field, residential development, or industrial development.” Maryland Department of Transportation Regression equations, Rational Method, WinTR-55, WinTR-20 used with GISHydro2000 tool McCuen et al. (2002) “The software listed herein have been approved for use as specified. The use of alternative programs is subject to approval by the Chief, Highway Hydraulics Division.” Massachusetts Department of Transportation Regression equations, Rational Method, WinTR-55, WinTR-20, HEC-HMS Martecchini et al. (2021) “Other standard engineering methods may be used subject to approval by the MassDOT Hydraulic Engineer. In general, results from several methods should be compared (not averaged) so as to identify the discharges that best reflect local project conditions with the reasons documented.” Table 2. (Continued).

Literature Review 23 State Agency Hydrological Modeling Tools and DRRMs Adopted Sources Excerpts and Comments Michigan Department of Transportation Regression equations, Rational Method, Michigan Department of Environmental Quality MDEQ-SCS spreadsheet model Michigan DOT (2006) “MDEQ has adapted the SCS method for use in Michigan (for calculation of peak flow only). The method referred to as MDEQ-SCS method is contained in the report Computing Flood Discharges for Small Ungaged Watersheds (Sorrell, 2001), which is included as Appendix 3-C.” Minnesota Department of Transportation Regression equations, Rational Method, WinTR-55, WinTR-20, HEC-1, Hydrain MnDOT (2000) “Suitable computer programs such as HEC 1, TR-20, TR-55, and HYDRAIN may be used for hydrologic calculations.” Mississippi Department of Transportation Regression equations and/or Rational Method Mississippi DOT (2001) “Detailed discussions of the hydrologic analysis process are provided in the AASHTO Highway Drainage Guidelines and Model Drainage Manual.” Missouri Department of Transportation Regression equations, Rational Method, NRCS UH method MoDOT (1972) “Small watersheds may be divided into rural and urban classifications... The Rational Method may be used on all watersheds smaller than 200 acres. On watersheds within the area limits shown in the table below, USGS Regression Equations may be used. The NRCS Unit Hydrograph may also be used for drainage areas larger than 6.40 acres.” Montana Department of Transportation TR-55, HEC-HMS, WMS-based models, NRCS UH MDT (1995) “The NRCS method in this section is consistent with HDS 2 and the source document NRCS TR-55. The method can also be used with a different procedure to produce hydrograph through software such as HEC-HMS, HEC-WMS, and TR-55.” Nebraska Department of Transportation Rational Method or Regression Equations, TR-55 Nebraska DOT (2015) “Figure 1 details the hydrologic analysis process that is typically followed by NDOR bridge hydraulics. If regression equation analyses are required (…) verify the drainage area size falls within the limits for each regression equations.” Nevada Department of Transportation Regression equations, Rational Method, HEC-HMS, HEC-1, WinTR-55, WMS-based models Nevada DOT (2006) “Synthetic modeling is used to develop peak flows or where a run-off hydrograph is required. Synthetic models using a unit hydrograph should not be used for watersheds over 100 square miles. The SCS (NRCS) unit hydrograph method shall be used to develop a unit hydrograph.” New Hampshire Department of Transportation Regression equations, Rational Method, HEC-HMS, TR-20 NHDOT (2014) “Deterministic Modeling - Method of analysis that strives to break down components of hydrology into physically based parameters. Typically these methods are used on ungaged watersheds and are most commonly contrasted with stochastic methods, which are based more on statistics.” New Jersey Department of Transportation Regression equations, Rational Method, NRCS TR-20, HEC-1, HEC-HMS, or others NJDOT (2015) “For drainage facilities which are designed to control volume of runoff, like detention facilities, or where flood routing through culverts is used, then the entire discharge hydrograph will be of interest. The analysis of the peak rate of runoff, volume of runoff, and time distribution of flow is fundamental to the design of drainage facilities. Errors in the estimates will result in a structure that is either undersized and causes more drainage problems or oversized and costs more than necessary.” New Mexico Department of Transportation Regression equations, Rational Method, HEC-HMS using NRCS UHs NMDOT (2018) “Computer models are the preferred approach for application of the SCS (now NRCS) Synthetic Unit Hydrograph Method. These computation methods make creation, addition, and routing of multiple hydrographs a relatively easy task. There are commercially available software programs such as WMS and Autodesk that perform hydrologic modeling. However, the NMDOT model of choice for large and/or complex watersheds and anytime a hydrograph is needed, is the U.S. Army Corps of Engineers (USACE) program HEC-HMS.” New York State Department of Transportation Regression equations, Rational Method, HEC-HMS, TR-20, TR-55, WMS NYSDOT (2021) “The existence of any detention features should be verified … These all have the effect of increasing the time of concentration, which may reduce the flow rate at the point under consideration downstream ... If the storage feature is close to the point under consideration, an analysis may need to be performed using HEC-HMS or another similar method to determine the proper flow rate. In some cases, detention features can reduce the required size of a downstream facility appreciably.” Table 2. (Continued). (continued on next page)

24 Resilient Design with Distributed Rainfall-Runoff Modeling State Agency Hydrological Modeling Tools and DRRMs Adopted Sources Excerpts and Comments North Carolina Department of Transportation Regression equations, Rational Method, Bentley GEOPAK Drainage, TR-55, TR-20, HEC models Chang (2016) “Natural Resources Conservation Service (NRCS, formerly Soil Conservation Service) methods, presented in TR-55 (49) and TR-20 (48), are recommended for hydrographic storage routing… Public domain software programs available from the Army Corps of Engineers Hydraulic Engineering Center (HEC) or NRCS are acceptable to perform hydrograph calculations and routing.” North Dakota Department of Transportation Regression equations, Rational Method (watersheds < 200 acres) NDDOT (2016) “The hydrologic methods to be used are listed below. If possible the method should be calibrated to local conditions and tested for accuracy and reliability… Deviations from these methods must be approved by the NDDOT Bridge Division.” Ohio Department of Transportation Regression equations, Rational Method, HEC-1, HEC-HMS, SWMM Ohio DOT (2022) “The hydrological modeling tools are cited in the context of the BMP design for post-construction stormwater management.” Oklahoma Department of Transportation Regression equations, Rational Method, TR-55 Oklahoma DOT (2014) “The peak runoff rate for design conditions is generally adequate for highway conveyance systems (e.g., cross drain, side drain, storm drains, open channels). However, if the design will include flood routing (e.g., storage basins, detention/retention pond, complex conveyance networks), a flood hydrograph is usually required. The development of runoff hydrographs (typically more complex than estimating peak discharges) will be based on the NRCS method.” Oregon Department of Transportation Regression equations, Rational Method, TR-20, TR-55, HEC-HMS Oregon DOT (2014) “The TR-55 hydrograph method produces its best results when used for small- to mid-sized basins. In addition, TR-55 cannot analyze some drainage features, such as diversions. Other methods are often used to calculate peak discharge rates and runoff hydrographs from larger or more hydraulically complex basins, such as the NRCS Technical Release No. 20, and the U.S. Corps of Engineers Hydraulic Engineering Center - Hydrologic Modeling System (HEC-HMS). These methods can also be used for smaller basins.” Pennsylvania Department of Transportation Regression equations, Rational Method, WinTR-55, HEC-1, HEC- HMS PennDOT (2015) “Countless hydrologic methods are available for estimating peak discharges and runoff hydrographs. The following sections list selected hydrologic methodologies. These methodologies, when properly selected and applied in engineering analyses, will be acceptable to PennDOT, and are preferable over equivalent alternative methodologies.” Rhode Island Department of Transportation Rational Method, TR-20, TR-55 RIDOT (2008) “The hydrological modeling tools are cited in the context of the stormwater management plan for pre- and post-development peak runoff discharge rates.” South Carolina Department of Transportation Regression equations, Rational Method, WinTR-55, HEC-1, SWMM, WMS-based models, among others SCDOT (2009) “If the drainage area contains a Carolina Bay, has a significantly large pond or lake, has a culvert(s) with significant storage volume upstream, or is very flat, the runoff must be determined by routing the floods through the basin and taking into account the storage. Unit hydrographs should be developed using the methods in references 22 and 23. The flows should be routed using an acceptable routing program.” South Dakota Department of Transportation Regression equations, Rational Method, WinTR-20 SDDOT (2011) “A consideration of peak runoff rates for design conditions is generally adequate for conveyance systems (e.g., storm drains or open channels). However, if the design will include flood routing (e.g., storage basins or complex conveyance networks), a flood hydrograph is usually required.” Tennessee Department of Transportation Regression equations, Rational Method, WinTR-55, HEC-1, HEC- HMS TDOT (2021) “Other hydrologic methods and software may be considered for use on TDOT projects at the discretion of the Design Manager at the request of the designer. For other hydrologic methods and software to be considered, the designer will need to demonstrate that the method is appropriate for the intended application.” Table 2. (Continued).

Literature Review 25 State Agency Hydrological Modeling Tools and DRRMs Adopted Sources Excerpts and Comments Texas Department of Transportation Regression equations, Rational Method, Hydrograph methods TxDOT (2019) “Watershed subdivision method is also applicable to complex watersheds, in which runoff hydrographs for multiple subbasins are computed, then routed to a common point and combined to yield the total runoff hydrograph at that location. TxDOT research on undeveloped watersheds (0-5822-01-2) has indicated that there is little justification for subdividing a watershed for the purpose of improving model accuracy.” Utah Department of Transportation Regression equations, Rational Method, TR-55 UDOT (2018) “Other hydrologic methods may be used, based on the complexity of the project. Submit a Deviation from Drainage Design Criteria form when other hydrologic methods are used, in lieu of what is listed in the UDOT DMOI. Document how the selected hydrologic method is appropriate and applicable to the watershed being modeled.” Vermont Agency of Transportation Regression equations, Rational Method, TR-55, HEC-HMS VTrans (2015) “The designer can choose to calculate the runoff characteristics by hand using the methods described in TR-55 or use free-ware or proprietary software. VTrans approves the use of the Hydrologic Engineering Center Hydrologic Modeling System (HEC-HMS), which is freeware produced by the USACE.” Virginia Department of Transportation Regression equations, Rational Method, WinTR-20, WinTR-55, HEC-HMS VDOT (2021) “Suitable computer programs such as the USACE’s HEC-HMS and the NRCS’ EFH-2, WinTR-55, and WinTR-20 may be used for the hydrologic calculations. The TR-55 method (now referred to as the NRCS Method and formerly as the SCS Method) has been found best suited for drainage areas between 200 and 2,000 acres.” Washington State Department of Transportation Regression equations, Rational Method, Hydrograph methods, Hydrological Simulation Program—Fortran (HSPF)-based model WSDOT (2019) “Additional hydrologic procedures are available including complex computer models, which can give the PEO accurate flood flow predictions. However, these methods, which require costly field data and large amounts of data preparation and calculation time, can rarely be justified for a single hydraulic structure. The HQ Hydraulics section shall be contacted before a procedure other than those listed above is used in a hydrologic analysis.” West Virginia Department of Transportation Regression equations, Rational Method, TR-20, WinTR-55, HEC- HMS, WMS- based models WVDOT (2007) “Computer programs available from government agencies and private businesses are also acceptable. When using computer programs, all input data and results must be presented in a format that is easily understood and acceptable to the Division of Highways.” Wisconsin Department of Transportation Regression equations, Rational Method, TR-20, TR-55, HEC-1, HEC-HMS WisDOT (2021) “(Hydrographs) are also used to show the hydrologic effects of existing or proposed projects. The urbanization of rural areas increases peak flows, which has and will continue to overtax existing downstream structures such as highway drainage facilities. Replacing such overtaxed facilities with larger or additional structures is one option, but designers should also investigate adding a detention basin(s) upstream of the problem structure.” Wyoming Department of Transportation Culvert Design System (CDS) model, including regression equation and a hydrograph method WYDOT (2011) “Hydrological discussion and CDS tool is presented in the context of culvert design.” Note: DMOI = Drainage Design Manual of Instruction Table 2. (Continued).

26 Resilient Design with Distributed Rainfall-Runoff Modeling Report title Reference Comments Hydrologic Tool Used Identify and Analyze Inundated Bridge Superstructures in High Velocity Flood Events Ahmari et al. (2021) The work studied hydrodynamic forces acting on bridge decks during flood events. The hydrological simulations performed in watersheds in the city of Austin and Harris County, TX, were performed using the HEC-HMS model. HEC-HMS Development of Site-Specific Hydrologic and Hydraulic Analyses for Assessing Transportation Infrastructure Vulnerability & Risks to Climate Change Thomas et al. (2020) This study used the precipitation in future climate scenarios to estimate flooding vulnerabilities in transportation infrastructure. This study compared hydrologic and hydraulic assessments that follow PennDOT’s design practices with an expanded assessment considering more intense and frequent precipitation under future climate scenarios using HEC-HMS. HEC-HMS Quantifying Mountain Basin Runoff Mechanisms for Better Hydrologic Design Woolridge et al. (2020) The work evaluated the active streamflow mechanisms for large historical storms and design storms in the Colorado Front Range and to propose methods to model these mechanisms. Selected watersheds were modeled using HEC-HMS and the Soil Moisture Accounting (SMA) algorithm. HEC-HMS Assessing the Impacts of Super Storm Flooding in the Transportation Infrastructure—Case Study: San Antonio, Texas Giacomoni et al. (2019) The work presents an investigation on bridges and roadway flooding that created large storms in two watersheds near San Antonio, TX. These studies included future climate scenarios, and applied HEC-HMS and GSSHA models to assess which countermeasures could mitigate these impacts. The study also recommended updates in design criteria. Assessing the Impacts of Super Storm Flooding in the Transportation Infrastructure—Case Study: San Antonio, Texas Estimating Future Changes in 100-Year, 24-Hour Flows on the Connecticut and Merrimack Rivers Palmer and Siddique (2019) This work presented estimation of future flows using large- scale hydrological simulation of the referred rivers, including future climate scenarios, to assess potential impacts to transportation infrastructure in Connecticut. The hydrologic modeling tool [NOAA’s Hydrology Laboratory-Research Distributed Hydrologic Model (HL-RDHM)] and scale of the modeled grid (4 km × 4 km) are larger than typical modeling efforts using DRRMs. HL-RDHM Computational Enhancements for the Virginia Department of Transportation’s Regional River Severe Storm Model: Phase II Morsy et al. (2019) This research improved upon the R²S² model following improvements and automated workflows and facilitating the HEC-HMS application of the model for Virginia roadways. Hydrological calculations were in the Chowan River and used HEC-HMS. Analysis and Potential Solutions to Sediment Deposition in Dean Road Bridge Watershed, Midland City, AL Vasconcelos et al. (2018) The research focused on understanding the causes and proposed remediation strategies for an aggradation process on a bridge in a rural watershed in Alabama. The inflows used in SRH-2D and HEC-RAS 2D simulations near the bridge crossing were obtained with HEC-HMS. HEC-HMS Evaluation and Prediction of Bridge Pier and Contraction Scour of Cohesive River Sediments in Tennessee Schwartz and Palomino (2018) The work focuses on the evaluation of scour processes in Tennessee bridges with cohesive soils. As part of the research efforts, long-term hydrological simulation of daily flows in bridge crossings were derived with HEC-HMS and converted to cumulative effective stream power. HEC-HMS Caltrans Climate Change Vulnerability Assessments: District 6 Caltrans (2018) This report presents a vulnerability assessment of highways in California District 6. This assessment includes various natural and weather-related hazards, and the climate change stressors were quantified using the Central Valley Hydrologic Model (CVHM), which in turn was developed by the USGS. CVHM Post Construction Storm Water Research: Informing TDOT MS4 Strategies by Quantifying Performance of Current Practices Hathaway et al. (2018) Stormwater management practices in roadways based on grassed swales were evaluated in a field study and modeled with the hydrological and water quality model Source Loading and Management Model for Windows (WinSLAMM). It was determined that the model was valuable to quantify the performance of this type of stormwater management practice and quantified field infiltration with an error less than 20%. WinSLAMM Spatial Sustainability Assessment of Green Stormwater Infrastructure for Surface Transportation Planning Zhang et al. (2018) This work investigated a watershed-scale implementation of green infrastructure in the context of surface transportation considering Life Cycle Analysis, Life Cycle Cost Analysis, and water quality modeling. The hydrological tool used in this work was SWMM. SWMM recommendations of Phase I, such as model accuracy Table 3. State and federal studies applying DRRMs.

Literature Review 27 Report title Reference Comments Hydrologic Tool Used Study of De-icing Salt Accumulation and Transport Through a Watershed Herb et al. (2017) The work presents a study to characterize the transport and accumulation of chloride due to road de-icing. Three widely available hydrological models were evaluated to model chloride transport: SWMM, HSPF, and GSSHA. It was determined that capturing snowmelt close to the source yields highest chloride concentrations and best removal potential. GSSHA, SWMM, and HSPF Storm Water Control Management & Monitoring Toran et al. (2017) This report evaluated the performance of current stormwater management control design and management practices along the I-95 corridor. Field and numerical investigation involved a variety of constituents in the stormwater and indicated plant species that were performing poorly in bioretention design. The hydrological simulations applied SWMM. SWMM Effective Post-Construction Best Management Practices (BMPs) to Infiltrate and Retain Stormwater Runoff Osouli et al. (2017) This study evaluated the performance of newly constructed linear stormwater BMPs in Illinois using field observations and numerical modeling. Different types of BMPs were considered in an idealized catchment to control the stormwater runoff from a 1-in. precipitation event. The hydrological tool used in the study was Personal Computer Storm Water Management Model (PCSWMM). PCSWMM Rainfall-Runoff Modeling for Improved Peak Flow Estimates in the Black Hills Area of South Dakota Hoogestraat (2017) Peak-flow frequency estimates in the Black Hills area of South Dakota are complicated by the occurrence of extreme flood events that do not fit typical statistical distribution. Thus, the rainfall-runoff modeling approach was applied to 18 drainage basins in the Black Hills using HEC-HMS with a goal of improving future peak-flow frequency estimates. HEC-HMS Computational Enhancements for the Virginia Department of Transportation Regional River Severe Storm (R2S2) Model Morsy et al. (2017) This report describes the work to perform improvements to the Regional River Severe Storm model, which is applied to perform flooding forecast. The model combines access to forecasted rainfall data from the National Weather Service, the hydrodynamic model 2D unsteady flow (TUFLOW), and hydrologic modeling results from HEC-HMS. HEC-HMS Improving Hydrologic Disaster Forecasting and Response for Transportation by Assimilating and Fusing NASA and Other Data Sets Liang (2017) The objective of this study was the development of the Hydrologic Disaster Forecast and Response (HDFR) system, aimed at evaluating impacts to transportation infrastructure. The approach uses near real-time hydro-meteorological data retrieval and applies the Variable Infiltration Capacity (VIC) hydrologic modeling package. VIC Design of Forebay and Micropool for Highway Stormwater Detention Basins Guo and MacKenzie (2016) This study proposed a new procedure to design a sediment forebay at the entrance of a stormwater detention basin in Colorado. As part of the study, SWMM was used to derive runoff hydrographs from sub-catchments. SWMM Developing a Bridge Scour Warning System: Final Report Young (2016) The report explores alternatives to provide a warning system for bridges in Kansas linked to flooding. The Distributed Hydrologic Model (DHM) created by the National Weather Service is cited as an alternative to provide flash flood warnings. National Weather Service (NWS) Distributed Hydrologic Model Permeable Concrete Pavements Hein and Schaus (2016) This technical brief presents an overview of permeable concrete pavement systems and their use. The hydrological models SWMM, WinSLAMM, and HEC-HMS are cited as alternatives to be used in the hydrological design of these pavements. SWMM, HEC-HMS, WinSLAMM Estimation of Watershed Lag Times and Times of Concentration for the Kansas City Area McEnroe et al. (2016) This research focused on the calibration of lag times and times of concentration for Kansas City areas, as these are related. Values for lag times for individual events were obtained by simulations performed with HEC-HMS. HEC-HMS Highways in the River Environment: Floodplains, Extreme Events, Risk, and Resilience: Hydraulic Engineering Circular Number 17 Kilgore et al. (2016) This design manual provides guidelines and approaches to quantify the vulnerability of transportation facilities in riverine environments. The document provides methods for quantification of the exposure of highways to extreme events considering climate change and hydrological non-stationarity. The documents reference a case study in which a DRRM was applied. CUENCAS Table 3. (Continued). (continued on next page)

28 Resilient Design with Distributed Rainfall-Runoff Modeling Report title Reference Comments Hydrologic Tool Used Monitoring the Effects of Birmingham Northern Beltline Construction in the Little Cahaba Creek Watershed: Final Report Vasconcelos et al. (2016) This study performed a field and numerical evaluation of the hydrological and water quality impacts of I-59N to a headwater stream in central Alabama. Hydrologic modeling applied SWMM and GSSHA, including interactions between surface hydrology and shallow groundwater. SWMM, GSSHA Relating Design Storm Events to Ordinary High Water Marks in Indiana Merwade and Saksena (2015) This study focuses on determining the relationship between Design Storm events and Ordinary High-Water Mark (OHWM), as the latter is used in the context of flood management. This work applied HEC-HMS for hydrological predictions that were subsequently used in HEC-RAS simulations of various rivers in Indiana. HEC-HMS Iowa’s Bridge and Highway Climate Change and Extreme Weather Vulnerability Anderson et al. (2015) This study objective included obtaining estimates of flood discharge for six bridges in Cedar and South Skunk River basins in Iowa, considering extreme weather and climate change. Hydrologic simulation was performed using the CUENCAS model. CUENCAS Development and Evaluation of Best Management Practices (BMPs) for Highway Runoff Pollution Control Zhang et al. (2013) This work presented a study on the feasibility of roadway BMPs using field scale techniques in Nebraska. As part of the work, the HEC-HMS model was applied to estimate the required precipitation to generate direct runoff or estimate flow rates where grab samples were taken. HEC-HMS Transport, Speciation, Toxicity, and Treatability of Highway Stormwater Discharged to Receiving Waters in Louisiana Sansalone (2013) The work focused on the characterization of stormwater runoff quality. Among the topics investigated in this work was the influence of hydrology on rainfall-runoff metal element speciation. SWMM was used for unsteady design storm and continuous hydrologic modeling. SWMM Evaluation of Design Methods to Determine Scour Depths for Bridge Structures Zhang (2013) This report summarizes the study on bridge scour for 7 structures in Louisiana applying HEC-18 and surveyed scour depth. The Water-Surface PROfile (WSPRO) model was used for hydraulic modeling and HEC-HMS for hydrologic simulation. HEC-HMS Evaluating Scour at Bridges: Hydraulic Engineering Circular Number 18 Arneson et al. (2013) This design manual presents the state of knowledge and practice for the design, evaluation, and inspection of bridges for scour. The document briefly cites HEC-HMS as a model that can be used to estimate the timing of the flood hydrograph derived from runoff of the watersheds. HEC-HMS Synthesis of Hydrologic and Hydraulic Impacts: Technical Report Joseph and Sharif (2012) The study focuses on hydrological and hydraulic (H&H) impacts to roadway drainage infrastructure, providing guidance in defining and mitigating such issues. DRRMs exemplified by HEC-HMS, SWMM, and GSSHA are cited as hydrological tools to quantify these impacts. HEC-HMS Feasibility of Integrating Natural and Constructed Wetlands in Roadway Drainage System Design Stansbury et al. (2012) This study determined the effectiveness of the existing stormwater BMPs to treat roadway runoff in Nebraska. A HEC- HMS model was created to represent the study area hydrology. HEC-HMS Future Flooding Impacts on Transportation Infrastructure and Traffic Patterns Resulting from Climate Change Chang et al. (2011) This report presents an investigation on the potential impacts of climate change on travel disruption caused by road closures in two urban watersheds in the Portland metropolitan area. Among other components, the work used an ensemble of PRMS climate change scenarios, and the DRRM Precipitation Runoff Modeling System (PRMS) from the USGS. Culvert Design for Aquatic Organism Passage: Hydraulic Engineering Circular Number 26 Kilgore et al. (2010) This document focuses on aquatic engineering passage, presenting stream simulation procedures, methods, and design best practices. DRRMs are cited as means to derive flow duration curves in streams and unit hydrographs. SWMM, HEC-HMS Table 3. (Continued).

Literature Review 29 Report title Reference Comments Hydrologic Tool Used Design Guidance for Low-Water Crossings in Areas of Extreme Bed Mobility Thompson et al. (2009) This report studied the mobility of coarser stream material in the context of low water crossings. Numerical modeling was used to demonstrate how areas subject to mobilization events could be identified, and HEC-HMS was used to model the hydrographs in Llano River watershed, TX. HEC-HMS Storm Duration and Antecedent Moisture Conditions for Flood Discharge Estimation McEnroe and Gonzalez (2003) This report focused on procedures to improve flood hydrograph simulations. Different combinations of modeling procedures and inputs were tested in flood simulations for 66 gaged watersheds in Kansas. The hydrological model applied was HEC-1. HEC-1 Highway Hydrology: Hydraulic Design Series Number 2, Second Edition McCuen et al. (2002) This document discusses the processes of the hydrologic cycle that are important to highways. SWMM is cited as an example to generate surface water inflows through continuous simulation. Models such as HEC-1 and HEC-HMS are used as a tool of watershed modeling for highway stream crossings. HEC-HMS modeling tools now include the prediction of areal flooding intensity and extents; supporting evaluations of bridge scour, aggradation, and sediment transport; and stormwater management and modeling. With key stressors such as climate change, more frequent intense storms, and sea- level rise, DRRMs pose as an important tool in the analysis of the vulnerability and resiliency of roadway infrastructure. Moreover, with more stringent environmental regulations, the integra- tion of DRRMs and other modeling tools is expected to provide more precise assessments of the impacts and mitigation strategies linked to roadway development. The literature review presented in this chapter focused on highway design manuals or guide- lines presented in state DOTs that pertain to hydrologic modeling practices. According to the information gathered in online searches, 50% of the state DOTs updated the design guidelines since 2015, although it is uncertain whether the hydrologic design guidelines therein were revised at the same time. Upon revising these guidelines, it was determined that 98% of the hydrologic modeling practices make direct reference to the Rational Method or regression equations. More than half (52%) of the state DOTs refer to the NRCS TR-20/TR-55 methods in their hydrologic practices. Regarding the use of DRRMs by state DOTs, 54% of the hydrologic design guidelines refer to these types of models, with the most referenced one being HEC-HMS (48%). Other DRRMs that were referenced included WMS-based models (20%), HEC-1 (22%), and SWMM (4%). WMS-based models and other commercial hydrologic tools were also referenced by state DOTs; however, they are not focused on in the present synthesis. An interesting observation is that, although SWMM is not frequently referenced in the design guidelines, the respondents of the survey indicated a much broader use of this tool, as shown in Chapter 3. This literature review also included reports accessed via the NTL, with focus on the documents that applied or referenced DRRMs in the context of roadway infrastructure in the past two decades. These documents were sponsored by federal entities and state DOTs, and most studies were performed by research centers linked to universities and private consultants. Almost half of the reports (47%) were published in the past 5 years, which indicates an acceleration of the application of DRRMs in the context roadway infrastructure. These applications were very diverse and often focused on using hydrologic modeling to assess vulnerabilities, improve roadway resiliency, and mitigate impacts of roads to the environment. The DRRM tool most frequently used in these reports was HEC-HMS (56%), followed by SWMM (19%). By comparison with the hydrologic design guidelines used by state DOTs, the variety of DRRMs that were used in these reports is larger, which is consistent with the research nature of some of these reports. Table 3. (Continued).

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The increased frequency of extreme rainfall events, inland and coastal flooding, and other water-related stressors poses challenges to roadway infrastructure.

The TRB National Cooperative Highway Research Program's NCHRP Synthesis 602: Resilient Design with Distributed Rainfall-Runoff Modeling documents the practices of state departments of transportation on the use of DRRMs and identifies state DOTs that have adopted DRRMs and the context in which these models are applied.

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