Variability of urban drainage area delineation and runoff calculation with topographic resolution and rainfall volume Open Access

As of 2018, more than half of the world's population, including at least 79% of the US population (US Census 2010; UNDP 2018), lives in urban areas. Anthropogenic development has resulted in extensive built environments that alter water resource management and natural flow regimes (Leopold 1968; Paul & Meyer 2001; Walsh et al. 2005). Quantifying stormwater runoff from this complex setting is required for dependable water resource design, flood risk assessment, and environmental management. However, the intricate nature of urban environments makes quantifying contributing drainage areas and their runoff volumes challenging.

Green stormwater infrastructure (GSI) systems are widely used stormwater management methods that rely on natural processes such as infiltration and evapotranspiration, in addition to the ‘grey’ stormwater infrastructure (e.g., sewer pipes), to mitigate the negative impacts of urban stormwater. In stormwater infrastructure design, delineated drainage areas are often used to define runoff volume for sizing. Getting the drainage area ‘correct’ is particularly important to appropriately sizing and designing a GSI, which often works as an independent decentralized treatment area. Conversely, a sewer pipe is typically a continually linked system, so bypass from one point of entry may be able to be collected at the next downstream location. The variability/error in determining runoff volume can be divided into errors associated with (1) area delineation and (2) runoff generation and routing.

The accurate drainage area of the inlet is a prerequisite for GSI design, including the calculation of loading ratios – a design guideline for sizing GSI for acceptable sediment and volume loading. The loading ratio is the ratio of the contributing directly connected impervious area (DCIA) to the GSI site area. DCIA is the portion of the total impervious area that is directly connected to the drainage system (USEPA 2014; Ebrahimian et al. 2016). For example, the Philadelphia Water Department (PWD) specifies loading ratios to establish the maximum acceptable sizes for appropriately maintained GSI systems (PWD 2021). Substantially more runoff into a GSI than designed can cause frequent overflow and erosion within the GSI, and potentially overburden GSI vegetation (Emerson et al. 2010). On the other hand, if a GSI receives substantially less runoff than designed, the vegetation within the GSI may not survive and the design will not be cost-effective (Tu et al. 2020).

Different drainage areas may be derived for GSI depending on the method of delineation and the horizontal resolution of the topographic data. Drainage areas may be estimated from design drawings (e.g., AutoCAD drawings), topographic maps, or field surveys performed during a storm event. While field surveys during storm events provide reliable results, relying on weather prediction to schedule a survey is challenging.

Topography is the key to determining where and how water will flow. In the United States, the United States Geological Survey (USGS), the National Resources Conservation Service (NRCS), the Federal Emergency Management Agency (FEMA), and many state agencies have provided topographic maps of the country. These topographic maps have been used for general hydrologic modelling but lack the level of detail that is often required for modern technical and regulatory applications (Russell et al. 2015), including GSI drainage area delineation. Water routing infrastructure, such as roadway surfaces, inlets, and curbs, coupled with hydraulic routing intricacies, further complicate drainage area delineation in the urban landscape (Krebs et al. 2014). The light detecting and ranging (LiDAR) datasets provide a finer range of resolutions and have been shown to result in more accurate estimation of drainage areas and stream networks than traditional theodolite-derived topographic maps (Vaze et al. 2010) or photogrammetric DEMs (Murphy et al. 2008), although photogrammetric imagery obtained from unmanned aerial vehicles has been successfully used to produce very fine-scale DEMs (grid cell size of several centimeters) (Leitão et al. 2016). However, LiDAR datasets present their own challenges, including high cost and computing power requirements (Sofia et al. 2013), as well as data processing needs, such as separating the ground from buildings, vegetation, and other objects (Maguya et al. 2014; Muhadi et al. 2020). Moreover, very fine-resolutions in DEMs have been reported to introduce errors by overanalyzing minor topographical features and adding noise to the model (Charrier & Li 2012; Sofia et al. 2013).

The optimal range of DEM resolution to delineate stream networks and floodplain boundaries has been investigated in mostly large or medium watersheds (over one hundred hectares) in agricultural and natural settings. For such large watersheds, coarse resolution DEMs in the range of 2–10 m were found to appropriately delineate general watershed boundaries and aid in rainfall–runoff modelling (Charrier & Li 2012; Sofia et al. 2013; Russell et al. 2015). Leitão et al. (2009) investigated the effect of varying DEM resolution on overland flow networks in larger urban catchments (100 ha range) and suggested an acceptable DEM resolution no coarser than 500 cm to adequately represent urban drainage features. However, few studies were reported that apply LiDAR delineation on small-scale watersheds and drainage areas, which represent many urban catchments, typically less than 6 ha and up to 35 ha (Rossman & Bernagros 2018). Resolutions in the 100–200 cm range have been suggested for such small urban catchments. Dongquan et al. (2009) and Warsta et al. (2017), for example, delineated urban watersheds ranging from 14 to 34 ha using a 200 cm resolution DEM and validated the results with observed runoff data from several rains with a stormwater management model (SWMM). Hosseiny et al. (2020) and Parece & Campbell (2015) have delineated watersheds for urban areas in Pennsylvania and Virginia, respectively, from 100 cm resolution DEM datasets, combined with spatial information on the stormwater conveyance systems. While fine-resolution spatial information and robust data models have the potential to greatly assist in delineating urban drainage areas, there may be a point where fine-scale data overcomplicates the landscape (Buakhao & Kangrang 2016).

Previous research has quantified the high sensitivity of urban flooding models to DEM resolution (e.g., Haile & Rientjesb 2005; Savage et al. 2016; Muhadi et al. 2020). De Almeida et al. (2018) demonstrated, for example, that very fine-scale (order of 100 mm) changes in elevation can lead to substantial differences in modelled flood inundation and flood flow patterns in the urban environment. In this study, we investigate whether the drainage areas of micro-basins delineated for the treatment volume directed to GSI are as sensitive to DEM resolution as the urban flooding models.

The CN is a function of land use, soil type, and antecedent moisture conditions and can conceptually vary from 0 to 100, although 98 is used as the practical upper limit for a completely impervious surface. The NEH provides guidance for calculating CNs from observed runoff and rainfall data and contains tables of CN values for different land uses, soil types, and moisture conditions (NRCS 2004). The initial abstractions (I_a) are equal to λS, with the initial abstraction ratio (λ) of 0.2 set forth in NRCS (2004) and routinely used when applying the CN method (Mishra & Singh 2004). Smaller λ values have been suggested in later empirical studies, including λ = 0.05 for urban watersheds. The tabulated CN values in TR-55 need to be recalculated if a λ value other than 0.2 is used (Hawkins et al. 2009; EWRI Curve Number Hydrology Task Committee 2017).

Numerous studies have discussed the limitations of the CN method (such as its high sensitivity to uncertainty in CN and disregard of rainfall intensity, antecedent moisture conditions, temporal distribution, and seasonal variations) and suggested exercising caution when applying the method to calculate runoff (Hawkins 1993; Mishra & Singh 2004; Fassman-Beck et al. 2016). Notably, CN numbers back-calculated from measured rainfall and flow data are highly variable and are often correlated (increase or decrease) with rainfall depth, especially at low rainfalls (Hawkins 1993; Soulis et al. 2009; Ebrahimian et al. 2018). It has been suggested that the CN method is most accurate when storage (S) is less than or equal to approximately twice the precipitation amount (Mishra & Singh 2004; Fassman-Beck et al. 2016). Modifications to the CN method have been recommended in later literature, including using locally calibrated CN values instead of standard tables and applying distributed, rather than composite or area-averaged CNs (Grove et al. 1998; Hawkins et al. 2009; EWRI Curve Number Hydrology Task Committee 2017). Moreover, there have been suggestions to retire the CN method and replace it with physically based methods such as Horton and Green–Ampt infiltration models (Hawkins 2014; Chin 2021).

Hydraulics of urban stormwater flow is not generally considered in most methods of runoff generation, including the CN method. In particular, urban inlet bypass can be important, especially at higher flow rates (Ampomah et al. 2021), and is widely acknowledged and discussed in the literature, frequently in the context of calculating the capture efficiency of various road inlet structures (FHWA 2009) and specifically for urban storm inlets (Comport & Thornton 2012; Russo & Gomez 2014; Li et al. 2019). Because inlet bypass can have a substantial effect on GSI design and performance, as well as on the downstream areas receiving the bypassed flow and urban flooding, there is currently a need for more research into inlet hydraulics (Ampomah et al. 2021).

The first objective of this study is to find an optimal range of DEM resolution required to delineate drainage areas contributing to a single GIS inlet in urban areas. For this purpose, we delineated drainage areas to establish loading ratios for five urban GSI sites in metro Philadelphia in southeastern PA, at multiple resolutions of topographic and LiDAR-based DEM data. We validated the delineated areas at three of the sites by combining the calculated areas with the rainfall and inflow records in the context of the design method, the CN method. The CN method was chosen despite its limitations because it is still one of the standard methods in hydrologic design and regulatory applications for GSI. It is, therefore, important to understand the implementation and potential errors associated with the CN method for urban GSI watershed delineation. The findings of the first objective facilitated the second objective of this study, to evaluate whether the CN method can adequately describe the runoff generated at the range of rainfalls observed at the sites as well as explore the interconnection between drainage area delineation, runoff generation, and, ultimately, to inform GSI design.

The ML site is an infiltration GSI in Philadelphia with an underground rock infiltration bed and a distribution pipe to deliver the runoff across five tree pits (planters with trees). The runoff from the impervious surfaces of the surrounding street and sidewalks is captured from both sides of the adjacent street by two inlets. Inflow is monitored with an area-velocity sensor at the entrance of the distribution pipe and precipitation is monitored with an on-site tipping bucket rain gauge (Tu & Traver 2018).

The Philadelphia Zoo site consists of two rain gardens connected by a grass swale. Most of the inflow comes from surface runoff of the adjacent street. Inflow enters the rain gardens through two curb cuts (one at each rain garden), with a berm adjacent to each curb cut directing the flow from the main street into the system. Inflow is monitored with H-flumes, pressure transducers at the inlet structures of both rain gardens, and the precipitation is measured on-site with two types of rain gauges (Nichols et al. 2021).

The Roosevelt Planters consist of four sidewalk planters and an infiltration bed. The runoff from the street enters the planters through eight curb cuts (two on each planter) and sidewalk runoff enters through cuts in the planter walls (Tu & Traver 2019). No precipitation or runoff data was available from the site for this study.

The IT site receives runoff from a portion of the 100% impervious top deck of the adjacent parking garage on Villanova University's campus. The IT was purposely constructed with a very high loading ratio (Table 1) to study clogging. Precipitation and inflow are monitored at the site (Mueller 2017). The remainder of the parking garage's top deck drains to the TT site, located on the other side of the parking garage. The TT is designed to capture 2.54 cm (1 in.) of stormwater and includes a vegetated swale, followed by two rain gardens and an IT. Although the flow record from the TT is not part of this analysis, its drainage area was also delineated and compared to the drainage area indicated on pre-construction computer-aided design and drafting (CAD) drawings.

The digital elevation model (DEM) resolutions used in this study are summarized in Table 2. The ‘very coarse’ 236 and 305 cm DEMs for all Philadelphia sites were produced with the Topo-to-Raster ArcGIS tool from 305 cm contour lines (Jahangiri et al. 2021) obtained from Open Data Philly (2015). The medium (98 cm) and coarse resolution (152 cm) DEMs were downloaded directly via PASDA (Pennsylvania Spatial Data Access 2019) and Philadelphia impervious surfaces shapefiles were obtained from Open Data Philly (2015). Publicly accessible elevation data was not available for the Villanova sites. DEMs for the Villanova sites were created from LiDAR data, obtained with a Leica RTC360 LT-3D terrestrial LiDAR scanner by Villanova University. The LiDAR was converted into 7.6 cm DEM, which was resampled (interpolated) to create coarser resolutions. Finer, 30 to 60 cm, DEMs for the Philadelphia sites were collected in 2016 with Trimble TX-5 terrestrial LiDAR scanner and processed with Trimble Realworks.

The Philadelphia GSI polygon file, inlet point file, and building polygons were downloaded directly from the Open Data Philly website (Open Data Philly 2018). The curb cuts and berms at the Zoo and Roosevelt were manually digitized from the ArcGIS basemap (Jahangiri et al. 2021). For the Villanova sites, the shapefiles for building footprints, GSI, and drainage inlets were created using an integration of campus maps, GPS surveys, and aerial photographs. The design DCIAs in Table 1 and GSI footprint areas were provided by PWD or estimated from drawings and GIS (Jahangiri et al. 2021).

Precipitation and runoff data were collected at 5-min intervals during each of the 38, 42, and 39 storm events at IT, Morris Leeds, and Zoo, respectively. Storms with a total depth of 6.5 mm or more were separated into individual events based on a 6 h dry period rule, where a storm was identified as a separate event if rainfall occurred after a 6 h dry period. To ensure previous rainfall did not impact the data collected from specific events, 1- and 2-day antecedent rainfall volumes were calculated.

In Phase 1, the DEMs were pre-processed to fill sinks with the ‘Fill Sinks’ tool and to incorporate or ‘burn’ known drainage features (i.e., buildings, parking garage walls, drainage inlets, and GSI features). Sinks or depressions in the DEM prevent the D8 algorithm used by ArcHydro from assigning a flow direction to the sink cell, which may result in incomplete drainage areas. To prevent this, DEMs are routinely smoothed to remove sinks (Li 2014).

The shapefiles for GSI footprints, berms, curb cuts, and drainage inlet points were buffered from 30.5 to 152 cm, depending on the drain size and raster resolution, to better represent the footprint of these storm water features (Table 3). The features' approximate heights above or below the ground level were added to the buffered shapefiles' attribute tables (Table 3). The buffered shapefiles were then converted to raster files matching the resolution of the corresponding DEM. The resulting rasters were added to or subtracted from the smoothed-based DEM to raise berms, walls, buildings, lower inlets, curb cuts, and GSI, using the ‘Plus’ or ‘Minus’ tool, respectively. All the outputs obtained using these tools were then merged into a single raster, using the ‘Mosaic’ tool (Jahangiri et al. 2021). This ‘burning’ of relevant drainage features into the DEM is intended to enforce proper local drainage even when the features were not picked up by the DEM (Leitão et al. 2009).

In Phase 2, flow direction and accumulation rasters were generated by ArcHydro's ‘Flow Direction’, and ‘Flow Accumulation’ tools, respectively. The Spatial Analyst's ‘Basin’ tool, with the flow direction raster as an input, was used to generate a raster of drainage sub- or micro-basins – sets of connected cells that contribute to the same pour point or sink. Pour points are the points where the water would pour from one basin into an adjacent basin, and sinks are the points of internal drainage where the water would accumulate inside a basin. The sinks were identified with the ‘Sink’ tool of Spatial Analyst.

In Phase 3, we defined the total drainage areas for each GSI as all the micro-basins that drain directly into a GSI or its inlets, as well as the micro-basins that drain into those draining directly into a GSI (Jahangiri et al. 2021). For the purposes of this paper, all draining ground surface area was included. Building footprints were excluded, because stormwater from the roofs was assumed to drain directly into stormwater sewers (Hosseiny et al. 2020).

The reasoning behind using the frequency-matched CNs is discussed in Hawkins et al. (2009), who suggest several techniques to account for the variability in CN, including ‘frequency matching’, where return period rainfall is paired with similar return period runoff events. It is most appropriate when the CN equation is used as a storm-to-runoff frequency transformer (Chin 2021). Hawkins (1993) reports that, when using frequency-matched CNs, 70% of small watersheds show a ‘standard’ pattern, in which the CN decreases as precipitation depth increases until an asymptotic relationship is reached, at which point the CN values begin to stabilize and plateau. This asymptotic CN is often used as a single CN value for the rainfall–runoff relationship at a site, although an exponential equation has also been applied to account for the CN-rainfall dependency explicitly (Hawkins et al. 2010; Ebrahimian et al. 2018; Chin 2021).

Finer resolutions allow drainage micro-basins to closely follow the landscape. The number of micro-basins within the defined area of interest consistently decreased at coarser resolutions for all Philadelphia sites, as the individual micro-basins became larger (Figure 5(b)), resulting in higher variation and increased variability of the calculated drainage areas. The average micro-basin area was largest at the coarse resolution for both Villanova sites with a general increasing trend for the TT but not for the IT; the variation was less consistent at finer resolutions than for the Philadelphia sites. The trend of decreasing detail at coarser resolution is also evident in the flow accumulation lines. As can be seen in Figure 4 for the garage, the lines become less branched and converge to fewer points at larger DEM cell sizes.

Some rain events, especially at ML, have produced CNs exceeding 100 (or runoff exceeding rainfall), which is not possible and could be attributed to measurement errors. CN ranges and mean and median values for low (6.4–12.7mm), medium (12.7–38.1 mm), and high (38.1 + mm) rainfall range for select resolutions are summarized in Table A1 of the Appendix, Supplementary Material.

Finding the optimal resolution to delineate urban drainage areas is a balance between picking up the relevant drainage features and topography while minimizing the computational costs, noise, and unwanted topographic fine details such as cracks and texture. For this study, the first jump in the delineated area occurred between fine (60 cm) and medium (100 cm) resolutions for Morris Leeds, and between the medium (100 cm) and coarse (152 cm) resolutions for the Zoo and IT. The Roosevelt drainage area was likely overestimated even at the fine (61 cm) resolution, but no finer resolution was available for comparison.

The main mechanism for the jump in the drainage area between the medium and coarse resolutions in this study was the failure of the pre-processing method to include some of the drainage features at the coarse resolution when the size of the features was smaller than the DEM resolution. For example, several of the storm sewer inlets and the downstream curb cut directing flow to the Zoo rain garden did not ‘burn’ into the DEM at coarse resolution, resulting in runoff directed into a downstream storm sewer inlet instead of the rain garden. Resampling (interpolating) the coarse resolution (152 cm) DEM to 100 cm for the Zoo site resulted in recapturing the ‘burned’ inlets and restoring the drainage pattern of the 100 cm DEM. It may, therefore, be beneficial to resample coarser DEMs to match the resolution of the drainage features.

The drivers for the change in the drainage area between the fine and medium resolutions were not obvious and could include the loss of relevant urban microtopography, such as the grading splitting road runoff in two directions at the centreline. We have attempted to connect the patterns in the delineated drainage areas to the site characteristics – median slope and percent imperviousness. However, no identifiable patterns were found (Table 1). A greater variety of sites may be examined in the future to establish the connection.

Smaller drainage areas are expected to be more sensitive to resolution than larger ones. For example, the total area draining into the IT is similar at the median and coarse resolutions, even though the coarse DEM resulted in no area contributing to the top right inlet (Figure 4). The source of DEM also plays a role. The drainage areas derived from the 200 and 300 cm DEMs in this study tended to be unrealistic (Figure 5). In addition to having a coarser resolution, these DEMs were derived from contour lines. Vaze et al. (2010) have found that the commonly available coarse DEMs derived from contour maps resulted in more loss of drainage detail than the coarse DEMs of the same resolution derived by resampling finer LiDAR DEMs. Other factors affecting urban watershed delineation from LiDAR data include vertical accuracy, ground classification (Muhadi et al. 2020), DEM interpolation method (Goulden et al. 2016), and the attribution of micro-basins that do not drain directly to a GSI drainage area. The latter is a subjective process involving the examination of flow lines and sink locations that could be further examined and automated in future research.

CN values calculated from the natural rainfall–runoff pairs (Figure 7(a)–7(c)) varied highly from storm-to-storm and exhibited a general decrease with increasing rainfall volume for all sites and resolutions, which contradicts the theoretical assumptions of the original CN method (CN independent of rainfall) but is consistent with the general patterns of decreasing CN with increasing rainfall volume observed by others (Hawkins et al. 2009; Fassman–Beck et al. 2016; Ebrahimian et al. 2018; Schoener et al. 2021). Recalculating the CNs with λ of 0.05 instead of 0.2 did not change the general trend and resulted in lower overall CN values and a wider range of CNs (Figure 7(d)).

Recalculating CN from frequency-matched rainfall–runoff data (Figure 8) did not change the overall trends. The pattern of calculated CN values, even after frequency matching, did not follow any of the three most commonly observed response patterns defined in Hawkins et al. (2009) for CNs calculated from frequency-matched rainfall–runoff data, where the most common ‘standard’ response is represented by an asymptotic decrease in CN with increasing rainfall, the ‘violent’ response is represented by an initial decrease in CN followed by an abrupt increase at some threshold rainfall depth, an asymptotical approach to a higher CN value, and the ‘complacent response’ is represented by a continuous decrease of CN with increasing rainfall without approaching an asymptotic value. The calculated CNs in Figures 7 and 8 decreased with increasing rainfall, then levelled off or increased slightly at medium rainfall (approximately 21–46 mm range), followed by further decreases in the observed CNs at all sites as the rain increased further beyond 46–60 mm.

Although the use of the calibrated CN values derived from local observed rainfall–runoff data instead of the generic tabulated values has been recommended in the literature (Hawkins et al. 2009; EWRI Curve Number Hydrology Task Committee 2017), the data-derived CN values should also be used with caution. The decreasing trend in the CN vs. rainfall relationship has been reported to result in underestimated runoff if the asymptotic CN is used to calculate runoff from a smaller rainfall (Chin 2021; Schoener et al. 2021). For example, Schoener et al. (2021) observed that the CN method underpredicted runoff when the onset precipitation rates were high before the initial abstraction in the CN method was satisfied. Conversely, calibrated CN values obtained from small rain events (which predominate in observed records at most sites) will overestimate runoff if used with a large rainfall (Fassman–Beck et al. 2016). Because the tabulated CN values were originally developed from peak annual rainfall events (Hawkins et al. 2009), they are more appropriate for use with larger storms. A single CN value for a site can be obtained from the observed data as an average or median value by minimizing a least squares objective function or as an asymptotic CN value (Hawkins 1993). It is also possible to define a relationship directly relating CN to the rainfall volume (Hawkins et al. 2010). However, the exponential relationships commonly used to fit the data assume the asymptotic ‘standard’ or ‘violent’ response and should be investigated further for their applicability to the observed urban GSI drainage patterns.

The average CNs, calculated from all the observed rainfall–runoff pairs, were 95 for the IT, 98 for the ML, and 89 for the Zoo, with the standard deviations of 4, 3, and 7, respectively (Appendix A, Supplementary Material). As expected, the Zoo site, which has the highest percentage of pervious area had the lowest CN and exhibited the highest variability in calculated CNs. The average CN of 95 was lower than would be expected for the 100% impervious IT, and was influenced by the low CN values at high rainfalls, potentially pointing to inlet bypass.

The trend in CN variability shown in Figure 10 can serve as a quality check to help evaluate the drainage areas delineated at different resolutions relative to each other by observing the plot of CN vs. rainfall in Figures 7 and 8: the more positive or negative the slope of the calculated CN vs. rainfall volume trend, the more overestimated or underestimated the drainage area, respectively. This supports the earlier conclusion that the drainage areas delineated from the finest resolution in this study are more likely to correspond to reality, while the areas calculated at a coarser resolution are likely to have been overestimated, because the latter exhibit more CN variation and lower CNs than expected from the site's land use. In theory, the drainage area can be varied in Equations (1) and (2 until a slope closest to zero is observed between the calculated CNs and rainfall, which would indicate the ‘true’ contributing area. However, as discussed earlier, biases inherent to the CN method produce sources of error that contribute to the observed downward trend of CN vs. precipitation excess (for example, see Hawkins's (2009) discussion on sampling bias and partial areas). However, with small, highly impervious catchments common for most GSI, these biases may become less significant.

Given the flaws in the CN method, it may be difficult to interpret the data-derived CN values in the light of physical processes. However, examining observed flow and rainfall data and comparing it to other watersheds in the context of CN formulation may lead to some insights about urban drainage. A factor not included in hydrologic models, such as the CN method, is the hydraulics associated with the increasing momentum of flowing water at higher storm volume and/or intensity (Ampomah et al. 2021). The rainfall characteristics, including intensity and duration, have been reported to have a substantial impact on the contributing drainage area and runoff losses for small urban watersheds (Ramier et al. 2011; Fletcher et al. 2013). The contributing drainage area for larger storms may become larger than that for small storms if the momentum of flow is sufficient to overcome surface friction and landscape barriers, which in turn effectively increases calculated CNs. This momentum increase may account for the observed ‘bumps’ at medium rainfalls in CN vs. rain curves in Figures 7 and 8. As the intensity and volume of the rain increase further, however, inlet bypass begins to play a role, effectively decreasing CN. We suggest that the second drop in CN after its initial stabilization that was observed in Figures 7 and 8 at high rainfall may be the result of water bypassing drainage inlets when the flow momentum is high. Other processes, such as rain ‘shading’ by urban structures, could add to the decreasing trend in CN. Further investigation is recommended to relate inlet bypass data, rainfall properties (such as intensity and duration) and watershed properties (such as imperviousness and slope) to CN behaviour in future work. Additionally, while this study used the total event inflow volumes for analysis, temporal distribution of rainfall, inflow, and outflow from GSI is important, particularly for catchment-wide management of the drainage systems. A future study comparing the results of this CN analysis to the output from models that employ more hydrologically and hydraulically appropriate methods (for example, the methods available in the SWMM, Hydrologic Engineering Center – Hydrologic Modeling System (HEC-HMS), and Hydrologic Engineering Center – River Analysis System (HEC-RAS) softwares) could help better understand the physical processes behind the observed data.

Hydrological models often entail considerable data and model errors (Kuczera et al. 2006). Results of this study are subject to uncertainty associated with physical measurements (rainfall, runoff, and LiDAR elevations), data processing (LiDAR data pre-processing and GIS workflow), and model assumptions of the CN method.

Even with the rainfall measured directly on-site at all locations, rain gauge measurements are affected by a variety of error sources, depending on rainfall intensity, weather conditions, and the instrument used (Cecinati et al. 2018). The temporal variability of the rainfall means that averaging the measured rainfall also results in error, although this error is expected to be small for the relatively small study areas. Flumes and orifices with pressure transducers that were used for flow measurement in this study have the potential to produce measurement errors, with the power equation for weir flow amplifying transducer measurement errors, especially at low flows (USBR Water Measurement Manual). In addition, the 5 min rainfall and flow measurement interval in the study may be insufficient to capture the peak rainfall or flow from storms with high intensity due to the small size of the drainage area.

While the LiDAR data were processed in a manner to minimize error and uncertainty, there is inherently some uncertainty in LiDAR data collection, pre-processing, and DEM calculation (Goulden et al. 2016).

Finally, the assumptions and biases of the CN method (such as the assumption of the initial abstraction is equal to 20% of the maximum potential water storage), add to the measurement uncertainty when calculating CN numbers from the observed flow and rainfall data.

The results of this study add to the research that puts into question the conventional methods of calculating urban runoff by combining a single estimate of the drainage area derived from available DEMs, surveys, or drawings and a single tabulated CN value. Despite the flaws in the CN method, delineated drainage areas and data-derived CN values can serve as a check on each other and provide additional insights into the flow dynamics at the site, with incorrectly delineated areas increasing variation in CN with rainfall, and CN trends potentially pointing to an inlet bypass or change in contributing areas with rainfall volume. LiDAR DEM, rainfall, and flow data from additional diverse urban sites should be evaluated at a range of resolutions to generalize these findings to all urban sites.

The main findings of this study are summarized as follows:

• Delineated area estimates can vary widely based on the quality of the input data (e.g., DEM resolution and available information on the drainage features) and the delineation procedure used.

• A preliminary conclusion based on the sites in this study is that the optimal resolution lies in the range of 30–100 cm: DEMs of 150 cm (5 ft) and coarser tend to not provide sufficient detail to accurately delineate urban drainage areas on the scale of individual GSIs and DEMs under 15 cm (0.5 ft) add to the processing cost without adding value to the delineation process.

• Adding or burning all known drainage features, including curbs, into a DEM and interpolating the elevation data to resample coarse DEMs to a finer resolution matching the resolution of the drainage features can improve accuracy of drainage area delineation even at a coarser resolution.

• The CN method with a single CN number for the drainage area does not adequately describe the observed rainfall and inflow record at the three sites in this study, even after applying the recommended remedial modifications such as varying the initial abstraction ratio λ and frequency-ranking of the rainfall and runoff.

• CN value is sensitive to drainage area estimation.

• The variation of CN with rainfall volume should be incorporated into GSI design to match the CN value with the intended design rainfall and to understand the error associated with GSI performance for storms outside of the design conditions.

• The findings of this study suggest an additional mechanism of inlet bypass for continuing CN decreases at high rainfall in small urban watersheds.

The authors are grateful to Philadelphia Water Department, Pennsylvania Department of Environmental Protection, and current and past Villanova graduate students who contributed data and insights into this research. Any use of trade, firm, or product names is for descriptive purposes only and does not imply endorsement by the authors.

Data cannot be made publicly available; readers should contact the corresponding author for details.

The authors declare there is no conflict.