Improving the Practice of Modeling Urban Hydrology

As stormwater practitioners, if asked, we would all say that we are interested in protecting our water resources and preventing flooding or erosion of downstream properties. We may even be aware that very low levels of urban development (5% to 15% impervious surfaces) have been shown to result in degradation of streams (Booth and Jackson 1997, Wang et al. 1997, Short et al. 2005). Yet, the quality of our waters is still drifting downward.

The reasons for the poor or declining state of our water bodies are many. These reasons include a lack of political will to implement development changes, assumptions that existing regulations and practices are sufficient, local economics (or lack of) driving other priorities, and inertia within the engineering community at large to adapt to new practices and products. This last reason is sometimes justified, but all too often we substitute skepticism or worse for prudence and the advancement of our profession.

Given our concerns and the challenge before us, would it be a surprise that everything you learned from your university or your mentor may not be enough? Unfortunately, there is often only a limited understanding among designers and reviewers of the hydrologic tools we commonly utilize. This observation is based on over a decade of experience as the principal author of several stormwater management manuals and current hydrologic design requirements of many state and local governments, and as a reviewer of many development submittals.

Reducing urbanization effects on our water resources is a challenge. Many studies have confirmed that urbanization has a greater impact on frequent events than on the rare flood events (ASCE 1993). Urbanization’s effect on hydrology typically results in the following:

The size of precipitation event necessary to generate runoff is lowered.
There is an increase in the peak runoff rate and volume, particularly from the smaller more frequent precipitation events.
There is an increase in runoff pollutant concentrations and loading (mass/surface area/time) to water bodies.

Hydrologic and hydraulic models used to implement the flow and volume control standards must be developed accurately to achieve watershed protection goals. Unfortunately, practitioners often don’t know, or have forgotten, the original assumptions and limitations of modeling programs. Often, no critical thought is applied to methods or practices that have become “standard.” In particular, the misapplication of hydrologic models designed for large flow (flood) events to the smaller rain events that dominate water-quality designs has lead to problems implementing rate and volume control strategies effectively. Consequently, urban runoff in particular is often underestimated, and resulting design discharge rates don’t mimic intended predevelopment conditions (Pitt 1999). Even if a community has design standards to protect stormwater quality and avoid nuisance flooding, their implementation is often poor from the beginning stages of design.

This article is intended to improve the current state of engineering practice regarding urban stormwater modeling through the following:

First, to provide a greater understanding of the challenges and assumptions behind the most common urban stormwater modeling methods, the Rational Method and the Curve Number (CN) Method (also commonly referred to as the SCS or NRCS method).
Second, to provide design guidance for developing a hydrologic model using the CN Method and, more specifically, developing curve numbers.
Third, to provide design guidance for the selection and use of methods for determining time of concentration. Time of concentration is the second most influential parameter in the CN Method, behind selection of CN values.

General Background of Hydrologic Models
The two main hydrologic models used for urban stormwater management are the Rational Method and the CN Method. The Rational Method (commonly attributed to Mulvany 1851) was developed in the 1800s to estimate peak flow rate (Q) of flood events. The Rational Method wasn’t developed to determine runoff volume or adequately deal with modeling runoff during smaller storm events that drive so much of stormwater quality issues. That’s not to say that many haven’t warped the model into other uses.

With the advent of computer-based hydrologic modeling software in the last century and improved models, the Rational Method is best left to its most common application—sizing storm drainage pipe. The Rational Method’s development to estimate flow rate, along with its simplicity and government acceptance, generally results in satisfactory pipe design. However, where suitable emergency overflows are lacking to provide flood protection at low points, alternative models are needed to model high water levels. Another common error is to over estimate catch basin grate inlet capacity, resulting in underutilization of pipe capacity.

The CN Method forms the theoretical basis for both the TR-20 and TR-55 models developed by the (then) US Department of Agriculture Soil Conservation Service (SCS), which is now the Natural Resources Conservation Service (NRCS). The TR-55 model is a tabular simplification of the TR-20 model, developed when computers weren’t as readily available (Fennessey 2001b). Given the prevalence of computers today, TR-20 and its variants among commercial software providers are the recommended modeling platform when utilizing the CN Method.

There are many different hydrologic models available. These other models and the two discussed above have been written about by more experienced engineers and researchers. I wouldn’t say that the CN Method is the best, but it is the most widely used and readily accepted in urban design. Its use and acceptance is based on its government origin, ease of use, and fundamental soundness.

CN Method
The CN method is an event-based model. It was not developed to model continuous simulations (multiple storm events) or snowmelt. The CN Method includes two distinct elements. The first element is the use of curve numbers to estimate the runoff volume from rainfall depth. Each CN has a constant rainfall to runoff transformational value. The second element is use of rainfall hydrographs to distribute rainfall depth and resulting runoff rate over time. The NRCS developed several hydrographs (Type I, IA, II, and III) to cover the entire United States. Some state and regional governments have also developed their own hydrographs for use.

To apply CNs for modeling runoff, it is important to understand the method’s limitations and basis of development. This understanding is particularly important for small precipitation depths (less than 3 inches or 76 mm). This depth happens to include most storm events in the western United States and all of the storm events typically associated with stormwater-quality and habitat degradation throughout the United States.

The accurate determination of CN selection, particularly when modeling smaller precipitation events, is necessary due to serious effect on runoff calculations (Grove et al. 1998, Hawkins 1993). The most common resulting error is underestimation of runoff volume. This error then affects everything from estimated runoff rates and high water levels to pollutant delivery and erosion concerns. Unfortunately, models of urban conditions are some of the most prone to underestimating runoff delivery for reasons discussed below.

CN Development and Application
The CNs were originally developed to predict runoff from relatively uniform agricultural landscapes, based on research conducted largely in the eastern and midwestern US (Woodward et al. 2002). These areas of the country receive almost all of their annual precipitation in the form of rainfall. A moderately sized storm event in these regions is large enough (e.g., typical two-year, 24-hour storm event exceeds 2.5 inches or 64 mm) that CNs typically approach a constant value with rainfall depth (Figure 1). In other words, the entire watershed is contributing runoff, initial losses have been satisfied, and runoff contribution from vegetated areas is a significant contribution to the total runoff volume from a watershed. Approximately 70% of watersheds fit the pattern of Figure 1 (Hawkins 1993).

When trying to model runoff from smaller storm events or landscapes that don’t meet the above criteria, the engineer, designer, or reviewer must be more careful in the approach. When only a portion of the watershed is contributing runoff, then the CN for the overall watershed (composite CN) will vary, typically decreasing with rainfall depth as shown on the left half of Figure 1. To address this scenario, the best and most defensible method is to break up a watershed into subwatersheds of similar runoff-generating potential. This is frequently referred to as the distributed CN approach.

Composite Versus Distributed CN Approach
There are two methods or approaches for estimating CN for watersheds having more than one hydrologic soil-cover complex. The two are commonly referred to as the composite CN and the distributed CN approach. The National Engineering Handbook, Part 630, Hydrology (NEH 630), Chapter 10, refers to the two approaches as the weighted-CN and the weighted-Q respectively.

A composite CN is an area-weighted average CN calculated for an entire watershed. In a distributed approach, polygons within a watershed are broken out based on runoff-generating potential. There is no CN averaging; rather, separate CNs are developed for each polygon and separate runoff values calculated (Grove
et al. 1998).

The most common approach is the composite CN. However, employing the distributed CN approach is necessary to avoid significantly underestimating runoff volumes when differences in CN values within a watershed are large or precipitation depth is small. The underestimation of runoff using the composite CN approach is a result of the nonlinear relationship between CN and runoff depth (Figure 2).

As shown on Figure 2, larger CN values generate significantly more runoff than lower CN values. When varying runoff generating soil groups are composited (averaged), the decrease in estimated runoff by lowering the high CN values to the average value is greater than the increase in estimated runoff produced by raising the low CN values to the average value (Grove et al. 1998). An example runoff calculation comparison between composite and distributed approaches assuming a hypothetical 20-acre (8.1-hectare) urban watershed is provided in Table 1.

As shown in Table 1, using a composite CN will significantly underestimate total runoff volume compared to a distributed CN approach (0.17 versus 0.55 acre-feet). The volume modeled using the distributed CN approach is more than three times that using a composite approach. The difference between the two approaches will be even greater with smaller precipitation amounts. This example demonstrates that to significantly improve our accuracy in modeling runoff generated by small precipitation events and from land with significantly varying runoff potential, the effort to use a distributed CN approach will be needed.

Stormwater management plans prepared for cities have typically been based on a composite CN approach for two main reasons:

Specific details of future development areas other than anticipated development density (e.g., units per area) are largely unknown.
Stormwater facility planning for flood control is based on large flood events (e.g., 100-year event) where calculated runoff volume differences between the distributed and composite CN approaches are assumed to be insignificant or within accepted range of modeling uncertainty.

The assumption behind the second point is true where the design flood event exceeds soil infiltration capacity and a significant portion of precipitation on green spaces is converted to runoff. Using the same hypothetical urban watershed modeled for Table 1, but under a 4-inch (102-mm) precipitation event, the runoff volume developed using the distributed approach would be approximately 11% more than that developed using a composite approach. The difference in runoff volume calculated from the earliest part of the precipitation event is nearly “washed out” by the overall amount of runoff
generated.

The continued use of a composite CN approach as the modeling basis for stormwater management plans and sizing of regional facilities for flood control is appropriate for many communities. However, to utilize a composite CN approach for site specific stormwater management design within a proposed development won’t be appropriate for most communities. To better address the water-quality impacts of urbanization on our water resources, designs beginning with stormwater modeling utilizing a distributed CN approach will needed.

Application of Distributed CN Approach
Under a strict distributed CN approach, there is no area-weighted averaging of CNs. A practical application of the distributed CN approach is to lump (composite) areas with similar CN values together (guideline CN range is less than or equal to 5). Ineffective impervious areas that are disconnected from runoff conveyance facilities may also be lumped together with more pervious areas. In general, the goal is to separate the watershed and modeling calculations into land uses that generate runoff during the smaller storm events and those that don’t.

Effective impervious areas are those connected to drainage conveyance facilities (e.g., roads, ditches, storm drainage pipe). I’ve included ditches as a conveyance facility. However, infiltration potential along the ditch bottoms in relation to annual runoff conveyance volume and watershed location could alter the conveyance role of a ditch. An example of an ineffective impervious area would be a tennis court in the middle of a park.

Most urban stormwater quality events are small, and runoff from these events is generated only from portions of a watershed (e.g., impervious areas, water surfaces, and wet soils near wetlands or streams). Therefore, the attention to developing a model using a distributed CN approach is needed. In arid and semi-arid regions of the country, the 100-year precipitation event may be what the eastern portion of the United States would consider to be a small to moderate-sized event. Consequently, in these more arid regions, models built only for flood modeling should consider use of a distributed CN approach as well.

Time of Concentration
One of the more typical areas for design contention for reviewers is development of Tc values, particularly for predeveloped conditions. For undeveloped watersheds, the Lag/Curve Number Method (see NEH 630, Chapter 15) is recommended for estimating time of concentration (Tc) due to its simplicity and relative consistency among users in developing Tc times (Fennessey 2001b). This method is found in most modeling programs. Again, one does need to be aware of the typical topography used to develop this method (similar to CN development). As a rule of thumb, caution is warranted for applying the Lag/Curve Number Method when average slopes exceed 6%.

For estimated runoff in post-development conditions or undeveloped watersheds with steeper topography, it is recommended to calculate Tc based on the Sheet Flow, Shallow Concentrated Flow, and Channel Flow (if applicable) Methods. All of these methods are described in the NRCS TR-55 manual, Urban Hydrology for Small Watersheds (see TR-55, Chapter 3) and found in most modeling programs.

The maximum length for sheet flow conditions should be limited to no more than 100 feet. This recommendation is based on research conducted since the TR-55 manual was published. Typically, the sheet flow length will be much less than 100 feet. Wherever individual flow paths begin merging (e.g., a swale), sheet flow ends and shallow concentrated flow begins. In my experience, in a typical urban environment, sheet flow conditions are typically less than 50 feet.

The NRCS Web site section on hydraulics and hydrology provides more information on limits of sheet flow application: http://www.wsi.nrcs.usda.gov/products/W2Q/H&H/H&H_home.html. The above is not a complete description of the CN method, its applications, or limitations. The NRCS Web site section on hydraulics and hydrology is a good source for technical references, including the National Engineering Handbook, Part 630, Hydrology.

Conclusions and Recommendations
Urban hydrology is an inexact and evolving science. However, to ignore advances in practice does our profession(s) little service and doesn’t help address the impacts urban environments have on our water resources.

As local governments, we should understand the hydrologic and hydraulic tools we use or require others to use to guide development of our built environment. We should have a strong and consistent review process managed by staff that is more capable in stormwater modeling and design than the average development firm. If this sounds challenging, then consider teaming with a capable engineering consultant to assist your review process. Look for a consultant that is dedicated to your community’s future and can provide long-term staff consistency.

Successful government consultants will want to stay at least one step ahead of local regulations and design practices. You won’t be able to lead a client to where they want to go or explain where they may want to go regarding water resources if you aren’t capable yourself.

Development consultants often have a difficult path navigating between their clients’ immediate goals and a community’s long-term goals. It is very tempting to focus only on the client’ goals, particularly if the regulator’s definition of quality engineering or planning is shortsighted. However, for the overall good of our professions and the community we live in, a little more foresight is often needed.

I hope this article will be beneficial to individual practitioners in improving our practice of urban hydrology by:

Providing background on the development of CN Method, curve numbers, and time of concentration calculations
Showing the importance of utilizing the distributed CN approach when attempting to model precipitation events outside the development background/assumptions used to develop CNs
Making recommendations regarding time of concentration development
Providing references for future reading, personal reference, and more detailed information

This article assumes that we want to protect our water resources and other natural resources. Despite our desire and hopes, there is inertia to overcome in adapting and changing to new circumstances, knowledge, or future winds. However, if we are to truly preserve our last best places, then change in how we manage ourselves and our environment and how we practice urban hydrology will be needed.

Author's Bio: Erik G. Peters, P.E., is a consultant, residing in Missoula, MT.