Water Resources Research

Field studies of the storm event hydrologic response in an urbanizing watershed

Authors


Abstract

[1] Dead Run is a 14.3 km2 urban drainage basin, which is a tributary to the Gwynns Falls, the principal study watershed of the Baltimore Ecosystem Study. Hydrologic response in urban watersheds is examined through analyses of rainfall and discharge observations from the Dead Run watershed during a 6 month period beginning in June of 2003. Rainfall variability for flash flood–producing storms in Dead Run can be quite large when viewed from a Euclidean perspective. When viewed from the perspective of a distance metric imposed by the drainage network of Dead Run, however, the spatial variability of rainfall is small. The drainage network structure diminishes the effects of spatial rainfall variability for storm event hydrologic response, resulting in Dead Run exhibiting striking uniformity of response to storms with contrasting spatial distribution of rainfall. There is large storm-to-storm variation in the event water balance of Dead Run. Variation is linked to antecedent soil moisture (from the pervious portion of the watershed underlain by urban soils), rainfall variability, and spatial heterogeneity of runoff production.

1. Introduction

[2] Dead Run is a 14.3 km2 tributary of the Gwynns Falls watershed (Figure 1), which is the principal study watershed of the Baltimore Ecosystem Study (BES) [see Band et al., 2001; Groffman et al., 2002; see also Beighley and Moglen, 2003; Nelson et al., 2005]. The storm event hydrologic response of urban catchments is examined through analyses of rainfall and discharge observations from the Dead Run watershed during the six month period beginning 1 June 2003. The study period contained an unusually large number of heavy rainfall events, which contributed to the record annual rainfall accumulation in Baltimore of 1574 mm, breaking the record set in 1889.

Figure 1.

Overview of the Baltimore study region. Background image is topography derived from USGS 30 m DEM. The basin boundary for the 14.3 km2 Dead Run watershed is outlined. Also shown are the basin boundaries for Gwynns Falls, the principal study watershed of the Baltimore Ecosystem Study (BES), and Baisman Run, the forest reference watershed for the BES. The Baltimore city boundary is outlined in purple.

[3] Urbanization typically results in increasing flood peak magnitudes and increased sensitivity of basin response to short-term rainfall rates. During the 6 month observing period, there were 10 events in Dead Run with flood peaks greater than 1 m3 s−1 km−2 (in order to compare flood magnitudes for basins of differing size, flood peaks will be expressed as a “unit discharge”, that is discharge divided by drainage area). By contrast, the largest unit discharge in Baisman Run, the forest reference watershed for the BES (drainage area of 3.8 km2; see Figure 1), during the 2003 observing period was 0.2 m3 s−1 km−2. There have been no flood events in Baisman Run during the 5 year BES observing period (1999–2003) with a unit discharge exceeding 1 m3 s−1 km−2.

[4] Questions which motivate this study include the following. How does structure of the urban drainage network affect storm event response? What are the elements of rainfall variability, both temporal and spatial, that control storm event response of urban watersheds? How do heterogeneities of land surface properties determine storm event response of urban watersheds? These questions are examined through empirical studies of storm event response in the Dead Run watershed.

[5] High-resolution (1 km horizontal resolution, 5 min timescale) rainfall fields play a central role in analyses of hydrologic response. In this study, rainfall analyses are based on volume scan reflectivity observations from the Sterling, Virginia WSR-88D (weather surveillance radar–1988 Doppler) radar and storm total rainfall accumulations from a network of 19 double-gauge platforms in the Dead Run watershed (section 2). The rainfall distribution for flood-producing storms in urban environments can exhibit large variability in time and space [Smith et al., 2002; Zhang and Smith, 2003; Smith et al., 2005]. Radar and rain gauge observations are used to derive high-resolution rainfall fields for all storm events during the 6 month observing period.

[6] Stream gauging observations in Dead Run were made at seven locations (Figure 2) with basin scales ranging from 0.2 to 14.3 km2. The U.S. Geological Survey (USGS) stream gauging station at Franklintown (Figure 2) provided discharge observations at 5 min time resolution. Two stream gauging stations (Figure 2), denoted DR1A (drainage area of 1.2 km2) and DR2A (drainage area of 1.6 km2), were installed in June 2003 and provided discharge observations at 1 min time interval. Staff gauges were installed at four additional locations (Figure 2). The Lord Baltimore, pond 841 inlet and pond 841 outlet stations are within the DR1A watershed. DR3A is located downstream of the confluence of DR1A and DR2A (Figure 2). Manual stage observations were made at these four stations for selected events, most notably for a thunderstorm system on 11 August and for Hurricane Isabel on 18–19 September (see section 4).

Figure 2.

Overview image of the Dead Run study region. Background image is high-resolution topography (1 m) from lidar. Surface stream network is shown in blue lines. Basin boundaries for DR1A, DR2A, and DR3A are shown. Rain gauge locations are indicated by stars. Stream gauging locations within DR1A at pond 833, pond 841, and Lord Baltimore are shown. A box containing the grounds of Woodlawn High School is shown.

[7] Spatial variability of rainfall is examined both from a conventional Euclidean perspective and through distance metrics that reflect the spatial structure imposed by the drainage network of the river basin (section 2). Analyses of rainfall variability that are tied to drainage network structure provide important insights on the role of the drainage network in diminishing the impact of spatial variability of rainfall on basin response [see Robinson et al., 1995; Rinaldo et al., 1995; Morin et al., 2001; Smith et al., 2002; Botter and Rinaldo, 2003; Snell et al., 2004; Saco and Kumar, 2004]. Rainfall and discharge observations are used to analyze the storm event water balance (section 3), with special emphasis on processes that control the storm to storm variability in the water balance and spatial heterogeneities in the storm event water balance of urban watersheds. Rainfall and discharge observations from Dead Run are used in section 4 to examine basin response through the geomorphic instantaneous unit hydrograph (GIUH) [see Rodriguez-Iturbe and Rinaldo, 1997]. Empirical GIUH analyses are also used in section 4 to examine storm event hydrologic response over basin scales ranging from 0.4 to 14.3 km2.

2. Rainfall Analyses

[8] Spatial and temporal variability of rainfall plays an important role in determining the response properties of urban watersheds [see, e.g., Smith et al., 2002]. In this section, analyses of rainfall variability are presented for storm events in Dead Run during the 2003 study period. Of particular importance for hydrologic response (section 4) is a measure of the spatial variability of storm total rainfall that is linked to the network structure of the drainage basin.

[9] Radar and rain gauge observations are used to derive rainfall fields for storm events in Dead Run during the 6 month period beginning 1 June 2003. The Dead Run rain gauge network consists of 19 double-gauge platforms (Figure 2). Storm total rainfall was collected for 35 storm events during the 6 month observing period. Volume scan reflectivity data from the Sterling WSR-88D (time resolution of 5–6 min and spatial resolution of 1 km in range by 1 degree in azimuth) were obtained for each storm.

[10] For the ith storm, Ri(t, x) denotes the rainfall rate (mm h−1) at time t, relative to the time origin Ui of the storm, and location x within the drainage basin. The domain of the basin is denoted A. The duration of the ith storm event is denoted Ti. The rainfall field for the ith storm is {Ri(t, x); t ∈ (0, Ti]; xA}.

[11] Rainfall rate fields {Ri(t, x)} are estimated by applying a Z-R relationship (R = a Zb; Z is the radar reflectivity factor in mm6 m−3) to reflectivity observations at volume scan times t1, t2, … and for spatial locations xj; j = 1, …, M, where xj denotes the center of the jth 1 degree by 1 km radar bin in the domain A and M is the number of radar bins. Analyses presented in this paper utilize the “convective” Z-R relationship for which a = 0.0174 and b = 0.71 [Fulton et al., 1998; Baeck and Smith, 1998]. The time-interpolated rainfall rate estimates at radar bin locations are given by linear weighting between volume scan times, i.e.,

equation image

for tj < ttj+1. This computation provides estimates at an arbitrary time t, but for locations fixed to the center of radar sample bins xk. The radar rainfall estimate for time t and location x, equation imagei(t, x), is obtained by an inverse distance-squared weighting of the observations from radar bins:

equation image

for

equation image

[12] The sample bias, Bi, for the ith storm is the ratio of the mean storm total rainfall at rain gauge stations to the mean storm total rainfall from radar at rain gauge locations, i.e.,

equation image

where m is the number of rain gauge stations (typically 19 for the Dead Run rain gauge analyses), xj is the spatial location of the jth rain gauge and Gij denote storm total accumulation (mm) for the ith storm from the jth gauge. Bias-corrected rainfall rate estimates are given by

equation image

[13] The dense network of rain gauge observations in Dead Run plays an important role in developing rainfall analyses that can be used for water balance analyses. Bias-corrected rainfall estimates using (5) can provide good representations of the spatial and temporal distribution of rainfall rate over the Dead Run watershed (see, for example, Figures 3 and 4) .

Figure 3.

Scatterplots of rain gauge accumulations and bias-corrected radar storm total accumulations (based on equation (5)) for the 12 June 2003 storm using convective and tropical Z-R relationships.

Figure 4.

Contour map of storm total rainfall (mm) for the 12 June 2003 storm based on bias-corrected radar rainfall estimates. Rain gauge locations are denoted by circles. The gray scale background depicts the distance function d(x) in meters.

[14] Storm total rainfall for the 12 June storm exhibits large spatial variability (Figure 4), relative to the scale of the Dead Run watershed. The spatial variability of storm total rainfall fields is characterized for the 25 events with basin-averaged rainfall accumulations exceeding 5 mm (Table 1) by the mean rainfall over the basin, maximum rainfall over the basin and the coefficient of variation of storm total rainfall. The coefficient of variation ranges from 0.05 to 0.82 (Table 1). For the 12 June storm (Figure 4) the CV is 0.49, the mean rainfall is 17.2 mm and the maximum rainfall over the basin is 34.3 mm.

Table 1. Storm Event Summaries for the 25 Events With Storm Total Rainfall Accumulation Exceeding 5 mma
DateMean Rain, mmMaximum Rain, mmCVNormalized Flow DistanceNormalized DispersionMaximum 15 Rain, mm h−1Maximum 60 Rain, mm h−1Peak Discharge, m3 s−1 km−2
  • a

    Summary characteristics include storm date, storm total rainfall (mm), maximum point rainfall accumulation over the basin (mm), coefficient of variation (CV) of rainfall accumulation, normalized flow distance, normalized dispersion, maximum 15 min basin-averaged rainfall rate, maximum 60 min basin-averaged rainfall rate, and peak discharge of Dead Run at the Franklintown stream gauge (expressed as a unit discharge, i.e., discharge divided by drainage area).

3 June17.117.90.110.560.994.03.10.26
7 June38.141.90.070.560.9215.510.61.71
12 June a17.234.30.490.571.0229.112.71.31
12 June b11.325.50.540.590.8514.94.70.47
17 June13.715.20.060.561.029.76.30.49
19 June a10.612.80.100.560.9915.17.30.81
19 June b8.69.90.080.561.0010.54.20.49
2 July34.941.70.070.561.0217.58.90.63
7 July5.215.60.820.601.079.23.50.26
23 July23.627.70.100.561.0117.013.10.93
28 July7.18.80.140.560.996.23.30.11
3 August8.713.20.280.531.049.93.70.24
9 August10.015.80.260.590.9930.910.00.70
11 August5.013.00.740.590.8413.65.00.31
16 August15.721.50.230.551.0119.27.60.36
22 August11.021.60.380.520.9639.111.00.59
1 September5.216.30.240.560.9416.15.10.17
12 September26.729.00.080.560.999.65.10.37
18 September64.973.70.110.540.9951.325.42.77
22 September73.385.70.110.551.0536.526.53.31
14 October41.348.00.110.560.9948.716.91.78
27 October53.956.60.050.561.0122.010.61.45
28 October27.929.20.020.560.999.47.20.85
5 November22.528.00.190.541.0254.617.11.68
19 November43.548.00.070.561.0130.413.52.00

[15] Variability of rainfall can also be examined relative to a distance metric imposed by the drainage network. The distance function {d(x); xA} is the flow distance (channel and “hillslope”) from point x within the basin to the outlet of the basin (Figure 4). The rainfall-weighted flow distance is

equation image

where the weight function is

equation image

and it represents the mean flow distance for an event. equation imagei is the mean flow distance, conditioned on the spatial distribution of rainfall for storm i. Uniform rainfall over the basin, i.e., wi(x) = ∣A−1, produces the mean flow distance:

equation image
equation image

[16] The normalized flow distance, Di, is the rainfall-weighted flow distance for event i normalized by the maximum flow distance, i.e.,

equation image

where

equation image

denotes the maximum flow distance to the basin outlet from a point in the basin (necessarily on the basin boundary).

[17] The rainfall-weighted flow distance dispersion is defined by:

equation image

The dispersion for uniform rainfall is given by

equation image

and the normalized dispersion is defined by Si = equation image. The normalized dispersion takes the value 1 for uniform rainfall, is less than 1 for rainfall characterized by a unimodal peak and can take values greater than 1 (for example, in the case of multimodal rainfall peaks in both the upper and lower basin).

[18] The mean flow distance equation image for Dead Run is 4.08 km and the maximum flow distance dmax is 7.31 km. The ratio of the mean flow distance equation image to the max flow distance dmax for Dead Run is 0.56. The uniform rainfall dispersion equation image takes the value 1.58 km for Dead Run.

[19] For the 12 June event, the rainfall-weighted flow distance equation imagei is 4.17 km and the normalized flow distance Di is 0.57. The normalized dispersion equation imagei for the 12 June event equals 1.02 and Si equals 1.61 km. Despite the large variability in rainfall over the basin for the 12 June event, the “conditional” distribution of flow distances, given the spatial rainfall distribution, was close to the distribution of flow distances in the uniform rainfall case. The mean flow distance on 12 June is only 2% larger than the mean flow distance in the uniform rainfall case. The dispersion of flow distances on 12 June was virtually unchanged from the uniform rainfall case.

[20] Analyses of the 2003 storms (Table 1; 25 storms with mean rainfall greater than 5 mm) show that the normalized flow distance Di takes values in a narrow range, 0.52 to 0.60, corresponding to a variation in the mean flow distance equation imagei from 3.80 to 4.39 km. The normalized dispersion takes values ranging from 0.84 (11 August; see section 4) to 1.05 (22 September), corresponding to dispersions ranging from 1.34 to 1.65 km. Despite the large variability in rainfall, when viewed from a Euclidean perspective, the variability is small when viewed from the perspective of a distance metric imposed by the drainage network. These results suggest that storm event response in Dead Run is strongly determined by drainage network structure, an issue that we will examine in more detail in section 4.

[21] Temporal variability of basin-averaged rainfall rate is summarized through the maximum 15 min and 60 min values (Table 1). As will be seen in the following sections, the characteristic response time for Dead Run at 14.3 km2 is approximately 1 hour. Temporal variability of rainfall at timescales less than 2 hours is of primary importance for basin response in Dead Run. All events with peak unit discharge exceeding 1.0 m3 s−1 km−2 were associated with peak 60 min, basin-averaged rainfall rates greater than 10 mm h−1. The three events with basin-averaged rainfall rates greater than 10 mm h−1 at 60 min time interval, but with peak discharge less than 1.0 m3 s−1 km−2 occurred during the 30 day period from 23 July to 22 August, suggesting that antecedent soil moisture plays a role in storm event response of Dead Run (see section 3 for additional discussion). The maximum unit discharges, which occurred on 18–19 September (2.77 m3 s−1 km−2) and 23 September (3.31 m3 s−1 km−2), were produced by storms with the largest basin-averaged rainfall rates at 60 min timescale, 25.4 mm h−1 and 26.5 mm h−1.

3. Storm Period Water Balance

[22] The Dead Run watershed was developed in the 18th century and agricultural land use dominated the basin until the middle of the 20th century. Rapid urban and suburban development has taken place since the 1950s, especially in response to construction of the Baltimore Beltway, which passes through the watershed and was completed in 1962 (Figure 2) (see also Nelson et al. [2005] for discussion of basin development and its impact on the channel network of Dead Run). A heterogeneous mix of industrial, commercial and residential land use characterizes the current state of the watershed. In this section, we examine the storm event water balance with particular focus on storm to storm variability in runoff ratio (ratio of storm event runoff to storm total rainfall) and spatial heterogeneities of the storm event water balance.

[23] Stream gauges were installed in the upper Dead Run watershed at stations denoted DR1A and DR2A (Figure 2) in June 2003. The drainage area for DR1A is 1.2 km2. For DR2A, the drainage area is 1.6 km2. Stage data were obtained from these stations at a time resolution of 1 min. Direct discharge measurements were made at each site during the summer of 2003 and used to derive stage-discharge rating curves. Discharge time series for DR1A and DR2A at 1 min time interval were computed from stage measurements and stage-discharge rating curves.

[24] To illustrate observations used for storm event water balance analyses, we describe rainfall and discharge measurements for a storm on 11 August 2003 (additional analyses of this event are presented in section 4). Rainfall for the 11 August event, which was concentrated in the northwestern portion of the basin, produced unit discharge peaks of 2.0 m3 s−1 km−2 at DR1A and 0.3 m3 s−1 km−2 at Franklintown (Figure 5). The basin-averaged rainfall accumulations obtained by time integration of the basin averaged rainfall rates illustrated in Figure 5 were 8.4 and 6.7 mm, respectively. Time integration of the discharge time series (Figure 5) results in runoff values of 3.9 and 2.0 mm for the two basins and runoff ratios (runoff divided by rainfall) of 0.46 and 0.30. Similar computations were carried out for each of the 35 storm events and used to examine the storm event water balance of Dead Run.

Figure 5.

Basin-averaged rainfall rate (mm h−1, solid line) and discharge (m3 s−1 km−2, circle line) on 11 August 2003 for (top) DR1A and (bottom) Franklintown. Basin boundaries and stream gauge locations are shown in Figure 2.

[25] The storm event runoff ratio for the 35 storm events in Dead Run ranges from less than 0.2 to more than 0.75. The striking variability in runoff ratio is linked to rainfall properties, antecedent soil moisture and heterogeneities of land surface processes, as described below.

[26] Seasonal trends in the storm event runoff ratio for Dead Run (Figure 6a), suggest that antecedent soil moisture plays an important role in basin response. The mean runoff ratio (estimated using a LOWESS smooth of runoff ratio [see Helsel and Hirsch, 1992]) has a minimum in midsummer during which mean runoff ratio drops to 30%. Mean runoff ratios in early June and during the Fall exceed 50%.

Figure 6.

(a) Storm event runoff ratio for Dead Run at Franklintown (14.3 km2) versus month for the 35 storm events. Solid line is LOWESS regression of runoff ratio versus time of year. (b) Storm total rainfall (mm) versus runoff ratio. Solid line is LOWESS regression line. (c) Storm total rainfall (mm) versus month. Solid line is LOWESS regression line. (d) Residuals in the LOWESS regression of storm total rainfall and time of year versus month.

[27] The runoff ratio is also dependent on the storm total rainfall. The nonlinear relationship between rainfall and runoff is reflected in the increasing runoff ratio with storm total rainfall (Figure 6b). There were pronounced seasonal trends in storm total rainfall distribution for 2003 (Figure 6c), with a higher frequency of large accumulation events in early summer and fall, than in midsummer. The seasonal variation in storm total rainfall promotes lower runoff ratios during midsummer, suggesting that seasonality of runoff ratio is tied in part to the seasonal distribution of rainfall.

[28] Even when the nonlinear relationship between rainfall and runoff is accounted for, there is still strong seasonality in the storm event water balance (Figure 6d). The residuals in the relationship between storm total rainfall and runoff (Figure 6b) show a pronounced seasonal variation (Figure 6d), similar to the seasonal variation in runoff ratio (Figure 6a). The seasonal variation in storm event runoff ratio is tied both to seasonality in rainfall distribution and to seasonality in antecedent soil moisture. Similar results are found for DR1A and DR2A (not shown).

[29] There are heterogeneities in the storm event water balance over the 14.3 km2 Dead Run watershed (Figure 7). The mean runoff ratio for DR1A of 0.53 for the sample period is 1.8 times larger than the mean runoff for DR2A (0.30). For the Franklintown gauging station, the mean runoff ratio is 0.47 (compare, for example, with results of Wigmosta and Burges [1997]).

Figure 7.

Storm total rainfall (mm) versus runoff (mm) for storm events in Dead Run during 2003 field season for (left) DR1A and DR2A and (right) Franklintown.

[30] Heterogeneities in runoff over the Dead Run catchment are associated with contrasting land use and cover. The impervious fraction (buildings, roads and parking lots) of DR1A is larger than in DR2A, 45.1% to 30.2%. The land use in DR1A is principally light industrial and commercial. DR2A has a larger concentration of residential development. In addition to larger impervious fractions, it is likely that DR1A has a higher fraction of “hydraulically connected” impervious cover than DR2A [see Bedient and Huber, 2002, and references therein].

[31] Soil hydraulic properties for the pervious portions of the Dead Run watershed are highly variable. Measurements of saturated conductivity were made with a Guelph permeameter [Reynolds and Elrick, 1985] at several locations. Along a transect at Woodlawn High School (Figure 2) that extends from an area of construction fill near the school to the Dead Run channel, estimated values of saturated hydraulic conductivity for 10 cm depths ranged from 13 mm h−1 to more than 100 mm h−1. In most cases, the 10 cm measurements were located above a highly compacted soil with very low saturated conductivity. Observations suggest that urban soils in Dead Run are characterized by high surface conductivities and sharp decreases in conductivity at shallow depth. This profile results in surface saturation building upward from the impervious layer to the surface during rainfall events with large accumulations. An impervious layer at 10 cm, a porosity of 50% and high conductivity soils in the upper 10 cm of the soil, for example, would result in a storage capacity of 50 mm. Variability in hydraulic properties of urban soils is poorly understood, but of major importance for the storm event response of urban watersheds.

4. Basin Response Properties

[32] Basin response properties for Dead Run are examined in this section through analyses of rainfall and discharge observations for the 2003 storm events. Analyses of basin response at the 14.3 km2 scale of the basin outlet focus on events with “simple” hydrographs characterized by a single discharge peak produced by a short period of rainfall. The role of rainfall variability and spatial heterogeneity of land surface properties for storm event hydrologic response is examined through analyses of discharge observations at basin scales ranging from 0.4 to 14.3 km2.

[33] A striking feature of storm event response in Dead Run is the uniformity of hydrograph response properties at 14.3 km2 scale for storm events with large contrasts in spatial rainfall distribution (Figure 8). The 12 June 2003 storm (Figures 3 and 4; see also Table 1) produced a 1.31 m3 s−1 km−2 flood peak in response to a short period of high rainfall rates in which peak basin-averaged rainfall rate was 29.1 mm h−1 at 15-min time interval (Table 1). The 5 November event produced a 1.68 m3 s−1 km−2 flood peak in response to a short period of intense rainfall in which peak basin-averaged rainfall rate exceeded 50 mm h−1 at 15 min time interval (Table 1). The 12 June storm produced 7.4 mm of runoff in response to 17.2 mm of rainfall (runoff ratio of 43%) and the 5 November storm produced 11.0 mm of runoff in response to 22.5 mm of rainfall (runoff ratio of 49%). The time between peak rainfall rate and peak discharge was 55 min for the 12 June event and 61 min for the 5 November event (Table 2). The rainfall distribution for the 12 June storm (Figure 3) was concentrated in DR1A; storm total rainfall ranged from more than 30 mm in DR1A to less than 10 mm in the southern portion of the basin. The rainfall distribution for the 5 November storm (Figure 9) exhibited a local maximum in the south central portion of the basin (34 mm) and a minimum in DR1A (14 mm).

Figure 8.

Basin-averaged rainfall rate (mm h−1, solid line) and discharge (m3 s−1 km−2, circle line) for Dead Run at Franklintown for the (top) 12 June 2003 storm and (bottom) 5 November 2003 storm.

Figure 9.

Storm total rainfall field (mm) for the 5 November 2003 storm.

Table 2. Summary of Response Time Analysesa
DatePeak Discharge, m3 s−1 km−2tp, mintd, minLag Time, min
  • a

    Summary characteristics include storm date, peak discharge (expressed as a unit discharge), peak time in the estimated GIUH tp, dispersion time td, and the lag time of the event, expressed as the time from peak rainfall rate to peak discharge for a selected set of events from 2003 for Dead Run at Franklintown (drainage area of 14.3 km2).

12 June a1.31585955
19 June0.81624066
23 July0.93664877
9 August0.70585860
11 August0.31683875
22 August0.59534051
5 November1.68544561
19 November2.00605267

[34] The storm event response of Dead Run for the 5 November event can be accurately reproduced with a simple distributed hydrologic model, using high-resolution rainfall observations (Figure 10). The Network Model [Morrison and Smith, 2001; Zhang et al., 2001; Giannoni et al., 2003; Turner-Gillespie et al., 2003] partitions the drainage basin into hillslope and channel components and represents discharge at the outlet of a drainage basin as

equation image

where Q(t) denotes discharge (m3 s−1) at time t (s), A is the domain of the drainage basin, x is a point within A, d0 (x) is the distance (m) from x to the channel network, v0 is the overland flow velocity (m s−1), d1 (x) is the distance (m) along the channel from x to the basin outlet, v1 is the channel flow velocity and M(t, x) is the runoff rate (m s−1) at time t and location x. The total flow distance from x to the basin outlet is d0 (x) + d1 (x), the sum of the overland flow distance and the channel flow distance (see Figure 4). The runoff rate M(t, x) (mm h−1) at time t and location x is computed from the rainfall rate R(t, x) using the Green-Ampt infiltration model with moisture redistribution [Ogden and Saghafian, 1997]. Calibration of the Network Model for the 5 November storm resulted in a channel velocity, v1, of 1.85 m s−1 a hillslope velocity v0, of 0.035 m s−1 and a saturated hydraulic conductivity Ks (the principal soil hydraulic parameter required for the Green-Ampt infiltration equation) of 2.0 mm h−1.

Figure 10.

Model (circles) and observed (crosses) discharge m3 s−1 for Dead Run at Franklintown during the 5 November 2003 flood.

[35] The geomorphological instantaneous unit hydrograph (GIUH), g(t), specifies the unit response of the drainage basin to an instantaneous pulse of runoff of unit depth [see Rodriguez-Iturbe and Rinaldo, 1997]. The preceding formulation of basin response through the Network Model leads to the following representation for the GIUH:

equation image

where Mδt(t, x) is equal to δt−1 (mm h−1) for t ∈ (0, δt] and 0 otherwise. The GIUH arises as the limit in (15) as δt decreases to 0 and can be estimated from (15) by setting the rainfall rate equal to (δt)−1 for a “short” interval (0, δt] and the saturated hydraulic conductivity equal to 0.

[36] The GIUH, g(t), can be interpreted as the probability density function of travel times to the outlet of the drainage basin. Storm event response properties of a drainage basin can be summarized through parameters derived from the GIUH. The peak time, tp, of the GIUH (the mode of the travel time distribution) is a natural measure of the characteristic response time of the basin. A measure of dispersion in the response time distribution of the basin (analogous to the interquartile range of nonparametric statistics) is the shortest time period containing 50% of the unit runoff,

equation image

The travel time distribution has an upper bound, the time base tb of the GIUH, which is given by:

equation image

[37] The GIUH for Dead Run (Figure 11), based on the estimated channel velocity and hillslope velocity from the 5 November event, has a peak time, tp, of 54 min. The dispersion of the GIUH, td, is 45 min. For the 12 June event, similar analyses result in a sample GIUH with a peak time tp of 58 min, a dispersion td of 59 min. The time base, tb, takes values close to 2.0 hours (for all events) and reflects the maximum time period between production of surface runoff in the basin and its contribution to discharge at the outlet of the basin.

Figure 11.

Dead Run GIUH at Franklintown based on 5 November 2003 model analyses. The GIUH is expressed in s−1.

[38] The uniformity in response between the 12 June and 5 November events (Figure 8) follows from the drainage network control on the distribution of flow distances, as reflected in the normalized flow distance and dispersion (section 2, especially Table 1). Despite the striking differences in the distribution of rainfall over the basin (Figures 4 and 9), the normalized flow distance was 0.57 for the 12 June storm and 0.54 for the 5 November storm (Table 1). The normalized dispersion for both events was 1.02 (Table 1). Storm event response properties at the 14.3 km2 scale of Dead Run are similar for the two events because the drainage network structure dictates that the distribution of flow distances is quite similar despite differences in the details of the rainfall distribution.

[39] Despite the marked similarities in response for the two events, there are differences in response that are due to the combined effects of heterogeneities in response properties over the 14.3 km2 basin (as described in the previous section and subsequently in this section) and the contrasting spatial distribution of rainfall. The 12 June storm is dominated by response properties in the northern basin, especially DR1A (Figure 2), and the 5 November storm is more strongly influenced by response properties in the central portion of Dead Run, with relatively less influence exerted by the DR1A subwatershed. The contrasting rainfall distribution for the two events does not lead to significant differences in the flow distance distribution over the basin, but it does result in different portions of the basin controlling the storm event response.

[40] Heterogeneities of rainfall distribution, basin response properties and response to events of different magnitude are reflected in rainfall and discharge observations for storm events on 19 June, 23 July, 9 August, 11 August, 22 August and 19 November (Table 2). Each of these events, like the 12 June and 5 November events are dominated by a single pulse of rainfall. The GIUH peak time ranges from a minimum of 53 min to a maximum of 68 min. The dispersion time td ranges from 38 min to 59 min. The smallest value of the GIUH peak time is associated with an event on 22 August, which was characterized by the smallest value of normalized flow distance of the rainfall field (Table 1). The longest peak time and shortest dispersion time are paired with an event on 11 August with the smallest normalized dispersion of the rainfall field, 0.84 (Table 1) and with a large normalized flow distance, 0.59 (Table 1).

[41] The preceding analyses of basin response concern the aggregate response of the Dead Run basin at the 14.3 km2 scale of the Franklintown gauge. Below, we examine the storm event hydrologic response of Dead Run through analyses of discharge observations at basin scales ranging from 0.4 to 14.3 km2. These analyses center on hydrologic response for storm events producing bank-full, or near-bank-full, flood peaks, with particular focus on the DR1A subwatershed (Figure 12). The 1.2 km2 watershed has 2 detention basins that control 60% of the watershed. Pond 841 has a drainage area of approximately 0.35 km2 and has a large impervious fraction (Figure 12). Pond 833 has a drainage area of approximately 0.35 km2 and has a smaller impervious fraction than pond 841 (Figure 12). There are no surface channels above ponds 841 or 833. The surface channel between the outfall of pond 841 and the DR1A gauge has tributary contributions from the storm drain network controlling the area downstream of Lord Baltimore and pond 841.

Figure 12.

DR1A drainage basin with details of 841 and 833 detention basins. See Figure 1 for location of DR1A within the Dead Run basin.

[42] Staff gauges were installed at three sites (pond 841 inflow, pond 841 outflow and Lord Baltimore; Figures 2 and 12) in the DR1A watershed and at one site (DR3A; Figure 2) downstream of the confluence of DR1A and DR2A. The Lord Baltimore station is immediately downstream of the 833 detention basin. Stage observations were made at pond 841 (inflow and outflow) and Lord Baltimore for the 11 August storm. For Hurricane Isabel (18–19 September), stage observations were made at pond 841 outlet, Lord Baltimore and DR3A.

[43] A stage-discharge rating curve was developed for the Lord Baltimore station, based on direct discharge measurements made over the course of the summer. This was used to construct discharge hydrographs for the 11 August storm (Figure 13) and for Hurricane Isabel (Figure 14). Direct discharge measurements were not made for the pond 841 stations. A power law stage-discharge rating curve was used for the pond 841 inlet in which the exponent of the rating curve was the same as for the DR1A station and the prefactor was chosen to provide the same unit discharge peak as for the 11 August peak at the Lord Baltimore station. The rating curve for the pond 841 outlet was chosen to have the same exponent as pond 841 inlet and a prefactor that resulted in mass conservation for the pond 841 basin. A rating curve for DR3A was constructed with the exponent for the DR1A gauge and a prefactor which resulted in the DR1A hydrographs and DR3A hydrographs producing equal runoff values (mm) for Hurricane Isabel. The “pseudorating curves” for the pond 841 stations and DR3A were derived primarily for graphical analyses of the timing of flood response in the pond 841 stations and DR3A, relative to other stations in the Dead Run basin (Figures 13 and 14).

Figure 13.

Discharge hydrographs in DR1A for the 11 August 2003 storm; DR1A, Lord Baltimore, and 841 inflow and 841 outflow.

Figure 14.

Discharge hydrographs for DR1A, DR3A, and Dead Run at Franklintown covering the second peak from Hurricane Isabel on 19 September 2003.

[44] The 11 August 2003 storm (see Tables 1 and 2) was an element of a mesoscale convective system that produced heavy rainfall over the Baltimore metropolitan region. Heavy rainfall over Dead Run was concentrated in DR1A (not shown). Significant flooding was also concentrated in the DR1A watershed (Figure 5), which had a peak discharge of 2.0 m3 s−1 km−2 at the gauge and a peak of 2.7 m3 s−1 km−2 at Lord Baltimore. The peak discharge in DR2A was less than 0.2 m3 s−1 km−2 and the Franklintown peak at the Dead Run outlet was 0.3 m3 s−1 km−2. Peak discharge in the DR1A channel reach between Lord Baltimore and the DR1A stream gauge was at or above bank-full discharge.

[45] Hurricane Isabel produced two discharge peaks in Dead Run at Franklintown (see Figure 14 for hydrographs of the second peak at DR1A, DR3A and Franklintown) with the largest peak discharge of approximately 2.7 m3 s−1 km−2. Two periods of heavy rainfall (0130–0230 UTC and 0400–0415 UTC on 19 September) were responsible for the two peaks. The second period of rainfall produced the largest basin-averaged 15 min rainfall rate for the Dead Run basin (51.3 mm h−1; see Table 1) and the largest flood peak in DR1A (5.7 m3 s−1 km−2). Storm total rainfall accumulations exceeded 60 mm over the Dead Run basin, with maximum accumulation of approximately 75 mm.

[46] In addition to heterogeneities in the storm event water balance described in section 3, there are also pronounced heterogeneities in the hydraulics of basin response over the 14.3 km2 Dead Run watershed. The timing of flood peaks at DR1A, the pond 841 stations, Lord Baltimore and DR3A were used in conjunction with extracted channel flow distances to compute the wave velocity at bank-full discharge for channel reaches upstream of DR3A. The wave speed through the pond 841 detention basin based on travel time measurements from the 11 August storm (Figure 13) and measured flow distance was 0.17 m s−1. The wave speed in the channel between Lord Baltimore and DR1A, based on both the 11 August and 18–19 September events was 0.7 m s−1. For the channel reach between DR1A and DR3A, the wave speed, based on the Hurricane Isabel measurements, was 1.7 m s−1. In each case, the wave speed is characteristic of storm response with peak discharge close to the bank-full discharge.

[47] The timing of flood response in DR1A is strongly influenced by the pond 833 and pond 841 detention basins (Figure 12; pond 833 is upstream of the Lord Baltimore stream gauge, see Figure 12). Although they control similar upstream areas and are designed to provide similar controls of downstream flood peaks, the hydrologic response of the two detention basins is quite different. Pond 833 is a nearly square basin in which a distinct alluvial channel short circuits the detention basin (Figure 12). Pond 841 is an elongated basin with dense vegetation and no pronounced channel (Figure 12). The discharge capacities of the outlet structures of pond 833 and pond 841 were not exceeded by either the 11 August or 18–19 September 2003 events, implying that surface properties of the detention basins provide hydraulic controls of flood wave propagation in these portions of the DR1A drainage network. Flood wave attenuation in pond 841 and rapid flow through pond 833 result in a nearly synchronous contribution to flood peaks at DR1A from the two detention basins. The rapid, initial rise in the 11 August and 18–19 September hydrographs at DR1A (Figures 5 and 14) is due to local contributions from the storm drain network downstream of Lord Baltimore and pond 841. This local rise, followed by an “in-phase” contribution from the two major detention basins, is a characteristic feature of DR1A storm event response.

[48] The scale-dependent response of Dead Run is characterized by the estimated GIUH (Table 3) at Lord Baltimore (0.40 km2), DR1A (1.2 km2), DR3A (3.5 km2) and at Franklintown (14.3 km2). The Lord Baltimore, DR1A and DR3A analyses were carried out in similar fashion to those presented above for Franklintown (and based on the 5 November storm). The Lord Baltimore and DR1A analyses are based on the 11 August storm and the DR3A analysis is based on the 18–19 September storm. The estimated channel velocities used in the GIUH computation increase systematically with increasing scale: 0.6 m s−1 at Lord Baltimore, 1.4 m s−1 at DR1A, 1.5 m s−1 at DR3A and 1.8 m s−1 at Franklintown. The estimated hillslope velocities decrease with scale: 0.3 m s−1 at Lord Baltimore, 0.2 m s−1 at DR1A, 0.05 m s−1 at DR3A and 0.03 m s−1 at Franklintown. The systematic dependence of basin response on scale, as reflected in the GIUH analyses, is closely linked to heterogeneities in hydrologic and hydraulic processes, which in turn are controlled by alterations of the land surface due to urbanization.

Table 3. GIUH Analyses for Lord Baltimore, DR1A, DR3A, and Franklintown, Summarized by Drainage Area, Peak of the GIUH, Peak Time tp, and GIUH Dispersion Time tda
 Area, km2Peak, s−1 × 10−4tp, mintd, min
  • a

    Peak of the GIUH is mode of the travel time probability density function.

Lord Baltimore0.415.2136
DR1A1.28.12311
DR3A3.53.34029
Franklintown14.32.65436

5. Summary and Conclusions

[49] The storm event hydrologic response of Dead Run has been examined through analyses of rainfall and discharge observations during a 6 month period beginning 1 June 2003. The observing period occurred during a year of record rainfall in the Baltimore metropolitan region. Dead Run, which has a drainage area of 14.3 km2 above the USGS stream gauge at Franklintown, is a tributary to Gwynns Falls, the principal study watershed of the Baltimore Ecosystem Study. Principal conclusions of this study are as follows.

[50] 1. The spatial variability of storm total rainfall for flash flood producing storms in urban watersheds can be quite large when viewed from a Euclidean perspective. The coefficient of variation of storm total rainfall for the 2003 storms in Dead Run ranges from less than 0.1 to more than 0.8. The normalized flow distance and normalized dispersion are introduced as tools for examining rainfall variability from the perspective of distance metrics imposed by the drainage network. Analyses of these variables for the 2003 storms illustrate that the drainage network structure diminishes the effect of spatial variability of rainfall on storm event response.

[51] 2. Storm event response of Dead Run at 14.3 km2 exhibits striking uniformity of response, as reflected in the analyses of the 12 June and 5 November events. Analyses of seven events with “simple hydrographs” and short duration rainfall forcing illustrate both the uniformity of response that underlies procedures like the GIUH, as well as the role of rainfall variability and spatial heterogeneity of basin response for variability in catchment response at the 14.3 km2 scale.

[52] 3. Variability in the storm event runoff ratio of Dead Run is large and depends on rainfall properties and antecedent soil moisture. Despite the relatively large impervious fraction of the basin, antecedent soil moisture plays an important role in the storm event water balance of Dead Run. This conclusion is supported by strong seasonality in runoff ratio (including analyses for which the effects of storm magnitude are included) and by the seasonal variation in flood peak magnitudes.

[53] 4. The mean storm event water balance of Dead Run varies over the 14.3 km2 watershed, as evidenced by a mean runoff ratio greater than 50% in DR1A and less than 40% in DR2A. The mean runoff ratio for the 14.3 km2 watershed is 47%. Spatial heterogeneities in the storm event water balance are linked to impervious cover, but factors related to hydraulic properties of urban soils also play an important role.

[54] 5. The storm event response of Dead Run, like most catchments, exhibits striking variability with basin scale. Heterogeneity of basin response is closely linked to the scale-dependent response of Dead Run. Analyses of catchment response for two events producing bank-full, or near bank-full, peak discharge, were used to examine heterogeneity of response in Dead Run and its control on scale-dependent flood response. Analyses center on the DR1A watershed, which provides a model system for examining the role of a system of storm water detention structures on basin response. This system is characterized by the hydrology and hydraulics of upstream area, detention basin and uncontrolled portion of the watershed. Analyses of the GIUH at basin scales ranging from 0.35 to 14.3 km2 illustrate the role of heterogeneities of catchment response on the peak time and dispersion of the basin response, as represented by the GIUH.

[55] 6. The combination of dense stream gauging, high-resolution radar rainfall estimates and storm total rainfall observations from a dense network of rain gauges makes it possible to examine the spatial variability and heterogeneity of the storm event water balance and response properties in the Dead Run watershed.

Acknowledgments

[56] The authors would like to acknowledge Steve Stewart and Andy Becker (Baltimore County Department of the Environment) for assistance in installing stream gauges at DR1A and DR2A, Gary Fisher (USGS) for assistance with stream gauging and interpretation of results, and Matt Ballantine and Jane Diehl for assistance in data collection and analysis. The research was supported by the National Science Foundation (NSF grants EAR-0208269 and EAR-0409501).

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