Modeling Suspended Sediment Concentration in the Stormwater Outflow from a Small Detention Pond

Krajewski, Adam; Sikorska, Anna E.; Banasik, Kazimierz

doi:10.1061/(ASCE)EE.1943-7870.0001258

Open access

Case Studies

Aug 10, 2017

Modeling Suspended Sediment Concentration in the Stormwater Outflow from a Small Detention Pond

Authors: Adam Krajewski [email protected], Anna E. Sikorska, Ph.D. [email protected], and Kazimierz Banasik [email protected]Author Affiliations

Publication: Journal of Environmental Engineering

Volume 143, Issue 10

https://doi.org/10.1061/(ASCE)EE.1943-7870.0001258

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Abstract

Detention ponds constructed in urban areas should perform two major functions: reduce flood flows and improve quality of runoff by trapping sediments and related pollutants. Providing tools for an efficient and low data–demanding assessment of pond performance can greatly support sediment management at the small catchment scale. This paper adopts the approach of a continuously stirred tank reactor (CSTR) to model the sediment concentration in the stormwater outflow from a small detention pond located in an urbanized catchment. The model is developed and tested using data sets of seven rainfall–runoff–suspended sediment events. Good agreement between observed and estimated outflow from the pond is achieved for both hydrographs and sediment graphs in calibration and validation. Thus results indicate that the present model due to its low data demand can predict sediment graphs at the outlet from such low-volume reservoirs.

Introduction

Suspended sediments (SS) are considered as stormwater contamination due to their direct and indirect impact on water quality (Rossi et al. 2005). In particular, the excessive amounts of SS in rivers cause silting of river beds, hydraulic structures, and reservoirs; increased flood risk at river mouths; and deterioration of water quality and consequent higher water treatment costs. Suspended sediments might also carry other pollutants—e.g., pharmaceuticals (Sikorska et al. 2012b), phosphate compounds (Hejduk 2011; Rodríguez-Blanco et al. 2012), heavy metals (Rivaro et al. 2011), or radionuclides (Walling 2006; Porto et al. 2014)—which, when deposited in ponds located along rivers or transported with the river discharge downstream, pose a threat to human and water environments (Nagy et al. 2002; Sikorska et al. 2012b). Hence a reduction of the sediment excess is necessary for maintaining good ecological status of rivers and for efficient operation of existing hydraulic structures (Rossi et al. 2005; Sikorska et al. 2015).

Efficient management of the sediment removal requires accurate models for assessing the actual sediment supply into rivers. However, providing such models is not easy because of the complex and multivariable mechanisms involved in the production and the transport of sediments in the catchment (Hrissanthou 1998; Chen and Chau 2016). Accordingly, solid particles are mostly eroded and washed off from the catchment’s surface during rainfall or snowmelt events, causing a notable increase in the solids concentration in watercourses during successive flood events (Egodawatta et al. 2009; Huang et al. 2007; Hejduk et al. 2006; Banasik and Hejduk 2014). This process is further triggered by riverbank and riverbed erosion (Trimble 1997; Banasik et al. 2012). These processes may be intensified due to the expected increase in the frequency and the intensity of rainfalls (Fiener et al. 2013; Pai et al. 2015), or due to extensive land use changes (Banasik 1994; Kijowska-Strugała 2015). Recent research has revealed that the amount of solids generated in urbanized areas can notably exceed the amount produced in corresponding agricultural areas (Chichakly et al. 2013; Ciupa 2009; Franz et al. 2014). Other sources of sediment emissions are untreated wastewater discharges from combined sewer overflows (Rossi et al. 2005).

Such a diffuse character of sediment production makes it difficult to model the sediment supply and efficiently manage the removal of the sediment excess at the catchment scale. Hence, instead of reducing sediments directly at their scattered sources, it appears to be more feasible to reduce their accumulated amounts at the catchment outlet, especially in the context of small to medium-size catchments (Ward et al. 1980). Existing small ponds located along the stream could be adopted for this purpose (Chichakly et al. 2013; Verstraeten and Poesen 2000). Such low-volume reservoirs, sometimes called detention ponds, are placed in urban watercourses for the purpose of reducing the peak flows (Brydon et al. 2006), although the removal of runoff pollutants is usually not considered and instead is seen as a desirable side effect (Gradowski and Banasik 2008). However, such low-volume reservoirs are capable of trapping 49–80% of suspended solids entering the reservoir (EPA 2002). The effective solid trap efficiency of a reservoir varies strongly depending on characteristics of the solids, of the inflow and the outflow, and of the reservoir and its specific outlet structure (Taap et al. 1982; Haan et al. 1994; Verstraeten and Poesen 2000). Carpenter et al. (2014) showed that by modifying the outlet structure and thus by increasing the residence time, it is possible to increase the solids removal from 39 to 90%.

Similar analysis of low-volume reservoirs located along streams are much restricted and the process of sediment trapping and transition through such low-volume reservoirs has gained little attention so far (Birch et al. 2006; Arias et al. 2013). Previous research on reservoir silting has focused mostly on large reservoirs located in agricultural catchments (e.g., Banasik et al. 1993; Łajczak 1995; Morris and Fan 1998; Sieinski 2011; Yang et al. 2014). In contrast, measurements of the solids transport in small urban catchments have been carried out only sporadically (Métadier and Bertrand-Krajewski 2012; Sikorska et al. 2015). However, smaller reservoirs are more problematic to model and maintain because of restricted recorded data and a fast silting pace (Madeyski et al. 2008; Haregeweyn et al. 2012). Indeed, small ponds can become 80% silted, which is considered as losing their entire capacity, after a few years of operation (Hartung 1959).

Consequently, currently available methods for modeling the sediment transition were developed and thus are mostly suitable for larger reservoirs, and their application to small ponds is often limited. These models can be grouped into three types: (1) black-box models, (2) white-box models (hydrodynamic models) and (3) grey-box models (conceptual models). The first group consists of simple models developed on the basis of input and output observations of a system response (reservoir). This group includes Brown’s (1943), Churchill’s (1948) and Brun’s (1953) equations which allow for determining a reservoir’s trap efficiency. However, these models might yield large errors (Michalec 2014), which in the case of small ponds often might exceed the estimated value. Therefore applying them to low-volume reservoirs has been advised against (Verstraeten and Poesen 2000). Other researchers (Banasik et al. 1993; Kluck 1997; Górski 1999; Tareala and Menédez 1999; Boogaard et al. 2017) have proposed hydrodynamic models which are based on the principle of mass conservation and momentum or energy conservation (for water and solids). However, this approach is time-consuming and laborious, because it requires solving a system of partial differential equations and determining numerous parameters. Models of the third group constitute a transitional form between black-box and hydrodynamic (white-box) models. They require a low number of parameters and therefore are less time consuming and less data demanding than white-box models, but they allow for a more reliable description of sediment processes than is possible with black-box models. Hence they are often applied in engineering practice.

Of the three aforementioned model types, conceptual models appear to be most promising for modeling low-volume reservoirs (Haan et al. 1994). In this respect, Wilson and Barfield (1984, 1985) proposed a model in which a reservoir is divided into several chambers of identical volume, with each chamber functioning as a continuously stirred tank reactor (CSTR). Verstraeten and Poesen (2001) further modified this assumption by dividing a reservoir into chambers of identical surface instead of volume. In terms of small detention ponds, Wallis et al. (2006) and Zawilski and Sakson (2008) proposed modeling low-volume reservoirs as single-chamber reservoirs.

This paper further adopts the approach of a single-chamber reservoir to model the suspended sediment concentration in the stormwater outflow from a low-volume detention pond located in a small urbanized catchment. Specifically, the paper improves description of sediment trapping in small ponds located in streams and provides a low data–demand approach for more-accurate modeling of the solids transition through such reservoirs. In this context, sediment solids transported and trapped by a small detention pond during rainfall events are of primary concern because these contribute the major amount of sediment solids produced in urbanized catchments. In particular, a CSTR model is applied to model the sediment transport with the runoff water discharged from the catchment surface into the pond and the sediment discharge at the outlet of the pond. The approach is illustrated with an example of a small detention pond located in Warsaw, Poland with data sets of seven recorded rainfall–runoff–sediment concentration events.

Data and Methods

Catchment, Detention Pond, and Gauge Stations

The catchment of Służew Creek (Fig. 1) is located in the southwest suburb of Warsaw, Poland and has been periodically monitored since the mid-1980s (Banasik 1987; Banasik et al. 1988). Previous research focused mainly on the rainfall–runoff process (Banasik et al. 2008, 2014; Sikorska and Banasik 2010; Sikorska et al. 2012a, c, 2013), and to a lesser extent on the runoff quality (Sikorska et al. 2015). The area of the entire catchment to its outlet in Wilanów Lake amounts to

54.8 {km}^{2}

, whereas the area of the analyzed subcatchment at the profiled Wyścigi Pond is

28.7 {km}^{2}

and closes with a low-volume detention pond (Wyścigi Pond). The catchment is heterogeneous in terms of land development; although the northern part has been strongly urbanized and is encircled by housing estates and the airport (where Służew Creek is enclosed in a conduit), the southern part remains less urbanized and is dominated by single-family houses, fields, wastelands, and woodlands. As is typical of lowland catchments in Poland, the catchment area is very flat, with inconsiderable land slopes (less than 0.5%).

Fig. 1. Locality map of the Służew Creek catchment

Wyścigi Pond (Fig. 1) is a low-volume detention pond located at the catchment outlet and directly along the stream. Because of complete loss of its capacity, the pond was renovated in 2007, when its basin was restored and deepened and new shores were formed. Outflow from Wyścigi Pond is currently controlled by a trapezoidal channel. At the normal pool level, the pond surface is 1.3 ha and its volume is

14500 m^{3}

. The length of the reservoir is 240 m and its maximum width 80 m. To establish the stage–discharge–storage relationship, during passage of flood waves, periodic field investigations were conducted which included measurement of water level and discharge and periodic acoustic measurement of the reservoir’s depth (Fig. 2). Although the pond was intended to cut the peak flows, from the very beginning of its operation it has had only a small influence on reducing peak discharges (Pietrak and Banasik 2009).

Fig. 2. Area and capacity curves for Wyścigi Pond, based on acoustic depth measurements conducted in May 2015

The catchment area is equipped with two stream gauges and four rain gauges. Rain gauges allow for determining the mean areal rainfall within the catchment. The two stream-gauging stations are located upstream and downstream of Wyścigi Pond. Both are equipped with staff gauges and water-level data loggers. During the analyzed period of 2014–2015, water-level records were verified weekly by manual staff-gauge readings. These corrected water levels were used to estimate stream flows according to the rating curves. The rating curves for both sites were established using a power-law function of Harlacher, which is considered to be the simplest and most commonly applied form of rating curve (Di Baldassarre and Claps 2011), and for single-segment cross sections is described as

Q = a {(H - B)}^{n}

(1)

In Eq. (1),

B

was determined based on the field measurements, parameters

a

and

n

were identified by using TableCurve 2D version 5.01 software by plotting water level–discharge pairs measured from 2014 to 2015 and fitting the curve (Fig. 3). Although the rating curves were relatively well defined for these two cross sections over the observation period, errors cannot be completely excluded and are discussed in the last section.

Fig. 3. Rating curves for the inflow and outflow cross sections of Wyścigi Pond

The stations are also adapted for manual sampling of suspended sediment probes in the main stream by means of a manual bathometer (Fig. 4). This device consists of a 1 L container and two pipes. One pipe carries water with sediment into the container, while the other pipe discharges air. The shape and dimensions of the bathometer used were equivalent to those developed and applied by the Polish Hydrological Service (Pasławski 1973; Brański and Banasik 1996). The water samples were manually collected during flood events at intervals of 2–3 h during the day until the end of the event (when the water level decreased again). The suspended sediment concentration in each sample was determined in the laboratory by means of gravimetric analysis.

Fig. 4. Scheme of manual bathometer for taking samples of water and suspended sediment

Recorded Rainfall–Runoff–Sediment Events

Water sediment samples were collected during the period 2014–2015, which resulted in seven recorded rainfall–runoff–sediment events (Table 1). The average rainfall over the catchment was computed according to the Thiessen polygons method. Polygon shapes and areas were established based on the locations of the four rain gauges (Fig. 1). For the analyzed data set, the average maximum inflow to Wyścigi Pond was estimated at

0.736 m^{3} \cdot s^{- 1}

, which was approximately 3.5 times higher than the mean inflow in the period 2009–2012 (

Q_{mean 09 - 12} = 0.216 m^{3} \cdot s^{- 1}

). The maximum outflow from the reservoir was estimated as being very close to the maximal reservoir inflow (for the same event). This observation suggests that the reduction of peak flood flows in this reservoir is insignificant, which confirms the results of Pietrak and Banasik (2009). The detention time for each event was calculated based on the centroid concept, i.e., as the time difference between the centroids of the inflow and outflow hydrographs (Haan et al. 1994). The detention time reflects the average water residence time in the reservoir; for analyzed events its mean value was 1.18 h. The average maximum effluent concentration of the suspended sediment (

26.0 mg \cdot {dm}^{- 3}

) was 83% lower than the average maximum concentration of the inflow (

154.3 mg \cdot {dm}^{- 3}

). The outflowing mass of sediment was significantly lower than the inflowing mass of sediment. These measures suggest that Wyścigi Pond has a strong impact on trapping suspended sediments during the passage of flood flows. These seven measured events were used in the further analysis. For most events the authors observed the first flush effect, i.e., most of the sediment load was washed off at the beginning of the flood event, as seen by the occurrence of the peak concentration prior to the peak discharge, which is shown in Fig. 5 for an example event on April 26, 2015.

Table 1. Characteristics of Recorded Seven Rainfall–Runoff–Sediment Events

Number	Date	Total rainfall, $P$ (mm)	Rainfall duration, $D$ (h)	Maximum inflow, $I_{\max}$ ( $m^{3} \cdot s^{- 1}$ )	Maximum outflow, $O_{\max}$ ( $m^{3} \cdot s^{- 1}$ )	Detention time, $T_{d}$ (h)	Maximum SS concentration in inflow, $C_{\max}^{I}$ ( $mg \cdot {dm}^{- 3}$ )	Maximum SS concentration in outflow, $C_{\max}^{I I}$ ( $mg \cdot {dm}^{- 3}$ )	Total inflowing mass of SS, $Y_{in}$ (Mg)	Total outflowing mass of SS, $Y_{out}$ (Mg)	Reduction rate of SS mass (%)
1	April 20, 2014	6.9	5.50	0.529	0.459	1.50	128.9	21.7	1.95	0.432	77.9
2	April 26, 2014	23.5	16.7	1.440	1.410	1.61	214.0	58.6	9.66	3.22	66.7
3	May 6, 2015	15.8	8.16	0.640	0.633	0.98	203.9	53.3	2.84	1.18	58.3
4	July 25, 2015	8.0	5.00	0.460	0.450	2.28	422.2	15.6	0.744	0.212	71.5
5	September 4, 2015	5.1	8.33	0.358	0.340	0.39	16.4	3.20	0.069	0.0053	92.3
6	September 6, 2015	19.0	23.5	1.045	1.040	0.57	58.4	17.8	2.21	0.736	66.6
7	September 26, 2015	15.6	18.3	0.677	0.639	0.90	36.5	11.5	0.604	0.213	64.7
Range		5.1–23.5	5–23.5	0.358–1.440	0.340–1.410	0.39–2.28	16.4–422.2	3.20–58.6	0.069–9.66	0.0053–3.22	58.3–92.3
Average		13.4	12.2	0.736	0.710	1.18	154.3	26.0	2.58	0.86	71.1

Fig. 5. Observed inflow discharge and sediment inflow to Wyścigi Pond and modeled and observed outflow discharge and sediment outflow for the rainfall–runoff event of April 26, 2015

Suspended Sediment Outflow Model for a Low-Volume Reservoir

Flow Continuity Equation

Determining the outflow hydrograph from the pond relies on the water balance and is computed by a mathematical calculation between inflow, outflow, and water storage. Because all these elements change during the passage of flood flows, the relation between them can be analyzed only for very short periods, i.e., instantaneous times (

d t

). If in the water balance for the reservoir the precipitation, evaporation, and filtration are all negligibly small, then at any point in time (

t

) the difference between the inflow to the pond [

I_{(t)}

], and its outflow [

O_{(t)}

] will be equal to the change in the water storage (

d S / d t

), which can be expressed as

\frac{d S}{d t} = I_{(t)} - O_{(t)}

(2)

Suspended Sediment Continuity Equation

Computing the effluent suspended sediment concentration relies on the reservoir outflow. The main assumption is that the reservoir forms a single-chamber CSTR. This means that the delivered solids are immediately distributed across the entire reservoir (complete mixing, equal concentration), and at the same time particle deposition takes place. Note that this can be assumed only for low-volume reservoirs. Thus the rate of deposited solids is proportional to the current amount of solids in the reservoir, whereas the solids concentration in the outflow is equal to the solids concentration in the reservoir. Given these assumptions, the suspended sediment continuity equation for the particle load passing through the reservoir can be formulated in the following manner (Huber et al. 2006):

\frac{d (V C^{I I})}{d t} = I_{(t)} C_{(t)}^{I} - O_{(t)} C_{(t)}^{I I} - K V_{(t)} C_{(t)}^{I I}

(3)

Considering Eq. (3) in the finite difference form and solving it for the effluent concentration gives

C_{t + Δ t}^{I I} = \frac{C_{t}^{I I} V_{t} + \frac{(C_{t}^{I} \cdot I_{t} + C_{t + Δ t}^{I} \cdot I_{t + Δ t})}{2} Δ t - \frac{C_{t}^{I I} \cdot O_{t}}{2} Δ t - \frac{K \cdot C_{t}^{I I} \cdot V_{t}}{2} Δ t}{V_{t + Δ t} (1 + \frac{K \cdot Δ t}{2}) + \frac{O_{t + Δ t}}{2} Δ t}

(4)

The model has only one parameter,

K

, and its calibration requires the observed suspended sediment concentrations for both inflow and outflow. The prediction requires the inflow and outflow hydrograph, inflow sediment graph, and reservoir stage–volume relationship.

Model Calibration: Efficiency of Reconstructing Pond Outflow

The flow continuity Eq. (2) was solved for the outflow from Wyścigi Pond with the use of the Puls routing method (Hann et al. 1994) by considering a small finite difference form (

Δ t = 0.5 h

). In order to determine outflow, the inflow hydrograph and a stage–discharge–storage relationship must be known. For Wyścigi Pond, these characteristics were established by field investigations.

To assess the model efficiency, observed and modeled outflow were compared using Nash-Sutcliffe (NS) efficiency, which is a common choice for modeling flood flows (Moriasi et al. 2007)

NS = 1 - [\frac{\sum_{i = 1}^{n} {(Y_{i}^{obs} - Y_{i}^{sim})}^{2}}{\sum_{i = 1}^{n} {(Y_{i}^{obs} - Y^{mean})}^{2}}]

(5)

The effluent concentration was calculated according to Eq. (4). Inputs to the model were the measured discharge inflow and outflow, suspended sediment concentration at the inflow to the reservoir, pond volume, and suspended sediment decay coefficient (

K

). The suspended sediment decay coefficient was determined by optimizing the NS efficiency for each event independently, which was calculated between the observed and the modeled suspended sediment concentration at the outlet of the reservoir. For sediment simulation, the same time step as for the flow simulation was assumed, i.e., 0.5 h.

Model Cross Validation: Efficiency of Predicting Pond Effluent Concentration

The predictive ability of a model is measured by testing it on a set of data not used during parameter estimation. However, there often are not enough data available to allow some to be kept back for testing (Hyndman 2010), as is often the case for small detention ponds. In such cases, to evaluate the performance of the model it is a common practice to use the leave-one-out cross validation (Refaeilzadeh et al. 2009). In this method, for a data set with

N

observed events,

N

equations are performed. For each equation,

N - 1

events are used for training and the remaining event is used for testing the model. This approach avoids model overfitting, i.e., fitting a model too closely to the peculiarities of a data set. In the analyzed case, because data on only seven events were available, cross validation was used to evaluate the efficiency of predicting sediment concentration at the outlet of the reservoir.

Results

Reconstruction of Recorded Flood Events

The model was calibrated for seven observed rainfall–runoff–sediment events. The NS values for outflow hydrographs and sediment graphs and the identified values of the sediment decay coefficient are provided in Table 2. Generally, the model achieved good agreement between observed and estimated outflow from the reservoir for both hydrographs and sediment graphs. However, more-accurate estimates were observed for hydrographs (

{NS}_{avg} = 0.913

) than for sediment graphs (

{NS}_{avg} = 0.722

). An example of the model application for inflow and outflow from the reservoir is presented in Fig. 5 for the event of April 26, 2014. The suspended sediment decay coefficient estimated from recorded data was on average

7.33 \times 10^{- 5} s^{- 1}

, but for the whole set of recorded events ranged from

3.20 \times 10^{- 5}

to

10.2 \times 10^{- 5} s^{- 1}

. This value should be interpreted as the fraction of sediment that is deposited in the reservoir in one second (Chapra 1997).

Table 2. Nash-Sutcliffe Efficiency for Predicted and Measured Hydrographs and Sediment Graphs and the Sediment Decay Coefficient of the Analyzed Events

Number	Date	NS for outflow		Suspended sediment decay coefficient, $K$ (optimized) ( $s^{- 1}$ )
Number	Date	Hydrograph	Sediment graph
1	April 20, 2014	0.967	0.638	$8.49 \times 10^{- 5}$
2	April 26, 2014	0.978	0.909	$9.00 \times 10^{- 5}$
3	May 6, 2015	0.827	0.675	$7.62 \times 10^{- 5}$
4	July 25, 2015	0.866	0.951	$10.2 \times 10^{- 5}$
5	September 4, 2015	0.776	0.427	$3.20 \times 10^{- 5}$
6	September 6, 2015	0.977	0.782	$6.60 \times 10^{- 5}$
7	September 26, 2015	0.996	0.670	$6.21 \times 10^{- 5}$
Range	—	0.776–0.996	0.427–0.909	$3.20 \times 10^{- 5} - 0.2 \times 10^{- 5}$
Average	—	0.913	0.722	$7.33 \times 10^{- 5}$

Sediment Decay Coefficient versus Detention Time

Plotting measured values of the detention time (

T_{d}

) versus identified values of SS decay coefficient (

K

) showed an increasing relationship for the analyzed data set (Fig. 6). This relationship was described with the use of the power formula

K = 7.11 \times 10^{- 5} \times T_{d}^{0.463}

(6)

with a high value of the coefficient of determination (

R^{2} = 0.859

). Parameters in Eq. (6) were estimated using Table Curve 2D software.

Fig. 6. Relationship between the suspended sediment decay coefficient and the water detention time

Representing

K

as a function of

T_{d}

and combining Eqs. (3) and (6) gives

\frac{d (V C^{I I})}{d t} = I_{(t)} C_{(t)}^{I} - O_{(t)} C_{(t)}^{I I} - K_{(T_{d})} V_{(t)} C_{(t)}^{I I}

(7)

Efficiency of Predicting Pond Effluent Concentration

Results from the cross validation are summarized in Table 3. Each fitted equation was characterized by a high coefficient of determination (

R_{avg}^{2} = 0.863

). The suspended sediment decay coefficient was predicted according to Eq. (6) in two ways: according to the detention time estimated based on the observations and on the modeled outflow hydrograph (Columns 6 and 7 of Table 3). The predicted average model parameters, based on the observed and the modeled hydrographs were, respectively, 2.14 and 28.0% higher than the average optimized parameter. Based on predicted model parameters, outflow sediment graphs were calculated again (an example event is shown in Fig. 7), and the observed and modeled effluent concentrations were compared using NS coefficient (Columns 8, 9, and 10 of Table 3). A strong decrease in the value of the NS coefficient was noticed when using the observed and the modeled hydrograph in prediction (

- 24.1

and

- 68.1 %

, respectively) for testing the event of September 4, 2015. For other events, the differences in the estimated NS coefficient values were less significant and therefore the average performance of the model in predicting independent events was good, with NS coefficient equal to 0.693 on average when using the observed hydrograph and to 0.621 when using the modeled hydrograph. In comparison, the average model performance for optimized events (NS

coefficient = 0.722

) was only slightly higher.

Table 3. Results of the Leave-One-Out Cross Validation

Number	Testing event	Estimated parameters in formula $K = a \cdot T_{d}^{b}$	Coefficient of determination $R^{2}$ for formula $K = a \cdot T_{d}^{b}$	SS decay coefficient, $K$ ( $s^{- 1}$ )			NS for outflow sediment graph with $K$
				Optimized	Predicted based on		Optimized	Predicted based on
				Optimized	Observed outflow hydrograph	Modeled outflow hydrograph	Optimized	Observed outflow hydrograph	Modeled outflow hydrograph
1	2	3	4	5	6	7	8	9	10
1	April 20, 2014	$a = 7.13$ $b = 0.464$	0.853	$8.49 \times 10^{- 5}$	$8.61 \times 10^{- 5}$	$9.61 \times 10^{- 5}$	0.640	0.627	0.524
2	April 26, 2014	$a = 7.10$ $b = 0.460$	0.844	$9.00 \times 10^{- 5}$	$8.84 \times 10^{- 5}$	$10.1 \times 10^{- 5}$	0.909	0.906	0.889
3	May 6, 2015	$a = 6.99$ $b = 0.479$	0.876	$7.62 \times 10^{- 5}$	$6.92 \times 10^{- 5}$	$12.4 \times 10^{- 5}$	0.675	0.670	0.413
4	July 25, 2015	$a = 7.15$ $b = 0.493$	0.804	$10.2 \times 10^{- 5}$	$10.7 \times 10^{- 5}$	$13.3 \times 10^{- 5}$	0.951	0.951	0.944
5	September 4, 2015	$a = 7.51$ $b = 0.350$	0.849	$3.20 \times 10^{- 5}$	$5.41 \times 10^{- 5}$	$7.23 \times 10^{- 5}$	0.427	0.324	0.136
6	September 6, 2015	$a = 6.78$ $b = 0.546$	0.946	$6.60 \times 10^{- 5}$	$4.97 \times 10^{- 5}$	$6.60 \times 10^{- 5}$	0.783	0.706	0.767
7	September 26, 2015	$a = 7.23$ $b = 0.446$	0.866	$6.21 \times 10^{- 5}$	$6.91 \times 10^{- 5}$	$6.43 \times 10^{- 5}$	0.670	0.661	0.676
Range		$a = 6.78 - 7.51$	0.804–0.946	$3.20 \times 10^{- 5} - 10.2 \times 10^{- 5}$	$5.0 \times 10^{- 5} - 10.7 \times 10^{- 5}$	$6.4 \times 10^{- 5} - 13 \times 10^{- 5}$	0.427–0.951	0.325–0.951	0.136–0.945
Range		$b = 0.350 - 0.546$	0.804–0.946	$3.20 \times 10^{- 5} - 10.2 \times 10^{- 5}$	$5.0 \times 10^{- 5} - 10.7 \times 10^{- 5}$	$6.4 \times 10^{- 5} - 13 \times 10^{- 5}$	0.427–0.951	0.325–0.951	0.136–0.945
Average		$a = 7.13$	0.863	$7.33 \times 10^{- 5}$	$7.49 \times 10^{- 5}$	$9.38 \times 10^{- 5}$	0.722	0.693	0.621
Average		$b = 0.463$	0.863	$7.33 \times 10^{- 5}$	$7.49 \times 10^{- 5}$	$9.38 \times 10^{- 5}$	0.722	0.693	0.621

Fig. 7. Predicted discharge and sediment concentration at the outflow from Wyścigi Pond for the rainfall–runoff event of May 6, 2015

Discussion

An approach of a single-chamber reservoir was proposed to model the SS concentration in the stormwater outflow from a low-volume detention pond using rainfall–runoff–sediment observations. Obtained results showed a good model fit between the observed and the modeled discharge and sediment outflow from the reservoir. This finding suggests that the model can reconstruct and predict the sediment graphs at the outlet of low-volume reservoirs.

However, the results of seven events showed that hydrographs were modeled slightly better than were sediment graphs. The reason for this could be related to different characterizations of calibration data used to establish both graphs. River flows were estimated using quasi-continuous observations recorded at regular time steps (30 min), whereas SS concentrations were evaluated based on irregularly taken manual samples usually limited to only a few samples per event. This could have an impact on the model calibration in three ways. Firstly, fewer data points were available for calibrating the model to sediment graphs than to hydrographs. Secondly, a limited frequency of the sediment samples may miss part of information on SS dynamics between the sampled records. Thirdly, the accuracy of discharge records is assumed to be higher than that of SS samples, which are susceptible to local and areawide fluctuations (Sikorska et al. 2015). In addition, errors in estimating the SS concentration in the water sample under laboratory conditions cannot be excluded. All these uncertainties may contribute to higher errors observed in sediment graphs than in hydrographs. Furthermore, the model is subjected to uncertainty due to its structure (simplistic description of the sediment trapping, assumption of ideal mixing across the entire reservoir), errors in observed data (mostly SS samples and to a lower extent discharge data), rating curves for deriving water level–discharge relationships (due to the rating curve form, errors in measurements of water level–discharge pairs, unstable conditions at cross sections, and so forth), which all should be quantified in future research. The later component especially may play an important role in the estimation of sediment concentrations for flood flows, for which discharge rating curves may be highly uncertain (Sikorska et al. 2013).

The observed relationship between the model parameter—the sediment decay coefficient—and detention time is in agreement with the commonly known and described phenomenon that the amount of deposited sediments increases with increasing water residence time in the reservoir, because sediment deposition patterns are related to flow patterns of the surface water (Stovin et al. 1999). This seems logical, because a longer transition time reduces the flood wave speed and thus facilitates the process of sediment settling. This issue was previously noted by other researchers (Zawilski and Sakson 2008) and was also observed in Wyścigi Pond during the seven analyzed events. This finding suggests a possible mechanism to increase sediment trapping in the reservoir, e.g., by modifying the outlet structure.

The model’s predictive ability was tested in two ways using a cross-validation approach. The first variant used the observed outflow hydrograph to predict the sediment graph, in order to investigate the impact of the proposed formula [

K = f (T_{d})

] on the modeled concentration. This variant corresponds to the common situation wherein only outflow from the reservoir are recorded and the sediment data are missing. The second variant assumed that both the outflow hydrograph and the outflow sediment graph were not available and thus both had to be predicted. Thus the outflow sediment graph was modeled from the modeled outflow hydrograph. Both variants obtained good model performance for six of the seven events, with a slight advantage of the first variant, as expected.

The poorer prediction observed for the event from September 4, 2015 could be caused by the limited number of samples available for this event (only three) and a particularly lower quality of data for this event due to a very low measured SS concentration (lower than

20 mg \cdot {dm}^{- 3}

) in comparison with other events (average

177.3 mg \cdot {dm}^{- 3}

). This might have caused higher errors in estimated SS concentration for this event than for other events. Generally, the measurement error of SS samples is assumed to be inversely proportional to the measured value, i.e., a higher error is expected for lower values due to increasing its relative contribution (Brański 1967). Apart from this one event, good coherence between measured and predicted sediment graphs was observed, which proves that the proposed formula for

K

estimation [Eq. (6)] can be successfully applied in further investigations on modeling the SS concentration at the outlet from the reservoir and for trapping SS in Wyścigi Pond.

The suspended sediment model for estimating concentrations in the outflow from the reservoir relies on the outflow hydrograph. This issue has clear implications in that the efficiency of predicting outflow hydrographs impacts the efficiency of predicted sediment graphs. However, this impact is difficult to directly quantify because it contributes to the estimation of the reservoir detention time, which is required for parameter identification, and to calculating the effluent concentration. As the results demonstrated, although the outflow from the reservoir was modeled very efficiently (

{NS}_{avg} = 0.913

), estimated detention times varied between the observed and the modeled hydrographs. For the analyzed events, average detention times were 1.18 and 1.98 h according to the measured and modeled hydrographs, respectively. Although the absolute difference between these two values was only 0.80 h, the relative difference was almost 40%. This difference was readily observed when the model was applied to events of May 6, 2015 and September 4, 2015 (Rows 3 and 5 in Table 3 and Fig. 7), where overestimated detention times decreased the quality of the model prediction. Regarding the event of May 6, 2015, a very irregular shape of the inflow hydrograph was observed which was difficult to model, and this inhibited a proper prediction of the sediment graph. Concerning the event of September 4, 2015, the lowest inflow over the analyzed period was recorded, which may have caused higher than average errors in the outflow estimation. This suggests that considerable errors may be expected in estimating the sediment graph for a low-volume reservoir with a relatively short water-residence time when the reservoir detention time is estimated from the modeled outflow. By contrast, for events with a high inflow (i.e., maximum event inflow a few times higher than the average) the uncertainty in sediment graph prediction was much lower. These findings show that the application of the model for weak events should be done carefully and may contain significant uncertainty.

The present approach was shown to be very sufficient for modeling the SS concentration in the outflow from low-volume detention ponds. However, its application requires defining conditions under which the assumption of a single-chamber CSTR is still adequate to represent a real system (reservoir). This issue requires further investigations. Based on this study, the model can be recommended for applications to reservoirs similar to or smaller than the tested Wyścigi Pond (i.e., surface area close to 1 ha, volume of

15,000 m^{3}

, length:width ratio of

4 ∶ 1

, and bottom surface slope approximately 1‰). However, application of the model to significantly larger reservoirs requires its verification. Thus before directly using Eq. (6) for model parameter estimation, it is recommended that the proposed approach be verified with measurements of inflow and outflow from the reservoir of interest and parameters be adopted accordingly.

The proposed model has only one parameter (sediment decay coefficient

K

), which can be estimated from only a few recorded events, and therefore is very flexible in application. Thus it could be adopted for modeling SS concentration at the outlet of other low-volume reservoirs. The only limitation of the method may arise from the fact that an observed sediment graph is required at the inlet of the reservoir. However, this observed sediment graph could be substituted with an additional model for modeling sediment supply from the entire catchment (Banasik and Walling 1996; Singh et al. 2008), for instance, by means of build-up/wash-off models (Sikorska et al. 2015). Moreover, the proposed model can be applied to existing or planned reservoirs. Because the detention time is implemented as a factor impacting sediment deposition, different variants (i.e., change in reservoir volume or type of the outlet structure) could be analyzed to support urban planning; landscape design; and decision-making processes in hydrology, environmental protection, and engineering. It should be kept in mind, however, that the method relies on the method of centroids for estimating the residence time of the reservoir, and thus is applicable for reservoirs without regulated or flattened outflows. Other concepts might be required for reservoirs with a constant or regulated outflow, i.e., when the peak in the outflow cannot be located. By reconstructing the pond outlet, it also must be remembered that a raised maximum water level might lead to a higher flood risk and therefore might not always be applicable. Thus any modification must be carefully analyzed and all its possible effects taken into account.

Conclusions

Based on the conducted field and model investigations, the following conclusions can be made:

1.

The analyzed low-volume detention pond (Wyścigi Pond) has a meaningful impact on reducing suspended sediment concentration in the stormwater outflow; however, it has a negligible influence on flood flow reduction. For seven analyzed events, the average maximum effluent concentration of the suspended sediment (

26.0 mg \cdot {dm}^{- 3}

) was 83% lower than the average maximum concentration of the inflow (

154.3 mg \cdot {dm}^{- 3}

), and the average maximum outflow from the reservoir (

0.710 m^{3} \cdot s^{- 1}

) was estimated as being very close to the average maximal reservoir inflow (

0.736 m^{3} \cdot s^{- 1}

).

2.

The model parameter—suspended sediment decay coefficient

K

—increases with rising detention time, i.e., the amount of deposited sediments is expected to increase with increasing water residence time in the reservoir.

3.

The presented approach can be applied to model the performance of Wyścigi Pond and to other similar low-volume detention ponds with natural or seminatural (i.e., without strongly regulated) outflows. This method is especially applicable to predict the pond effluent concentration and the trap efficiency during passage of flood events or to reconstruct the sediment graphs from recorded outflow hydrographs. The application of the method to reservoirs with a regulated constant outflow is limited.

4.

The application of the model to average and intense rainfall events is recommended. Application to weak events may yield high uncertainty in predicted sediment graphs, especially when both hydrograph and sediment graph have to be predicted.

5.

The possibility to investigate variants of reservoir settings (i.e., change in reservoir volume or type of the outlet structure) has potential in supporting urban planning; landscape design; and decision-making processes in hydrology, environmental protection, and environmental engineering.

Notation

The following symbols are used in this paper:

$a$: rating curve parameter;
$B$: water level at which discharge is equal to zero (cm);
$C_{(t)}^{I}$: suspended sediment concentration in inflow ( $mg \cdot {dm}^{- 3}$ );
$C_{(t)}^{I I}$: suspended sediment concentration in the reservoir and in outflow ( $mg \cdot {dm}^{- 3}$ );
$d S / d t$: change in water storage ( $m^{3} \cdot s^{- 1}$ ), at time $t$ ;
$d (V C^{I I}) / d t$: change in the suspended sediment mass in the reservoir ( $mg \cdot s^{- 1}$ ), at time $t$ ;
$H$: water level (cm);
$I_{(t)}$: inflow ( $m^{3} \cdot s^{- 1}$ );
$I_{(t)} C_{(t)}^{I}$: suspended sediment mass entering reservoir ( $mg \cdot s^{- 1}$ );
$K$: suspended sediment decay coefficient–model parameter ( $s^{- 1}$ );
$K_{(T_{d})}$: suspended sediment decay coefficient, dependent on detention time ( $s^{- 1}$ );
$K V_{(t)} C_{(t)}^{I I}$: mass of suspended sediment deposited in the reservoir ( $mg \cdot s^{- 1}$ );
$n$: rating curve parameter;
$O_{(t)}$: outflow ( $m^{3} \cdot s^{- 1}$ );
$O_{(t)} C_{(t)}^{I I}$: suspended sediment mass leaving reservoir ( $mg \cdot s^{- 1}$ );
$Q$: discharge ( $m^{3} \cdot s^{- 1}$ );
$T_{d}$: detention time (h);
$t$: previous time step;
$t + Δ t$: new time step;
$V$: reservoir volume ( $m^{3}$ ), $V_{(t)} = S_{(t)} + V_{NPL}$ ;
$V_{NPL}$: reservoir volume at normal pool level ( $m^{3}$ );
$Y_{i}^{obs}$: $i$ th observed value;
$Y_{i}^{sim}$: $i$ th simulated value;
$Y^{mean}$: mean of observed data; and
$Δ t$: duration of the time step (s).

Acknowledgments

This research was supported by the National Science Centre, Poland under Grant 2015/19/N/ST10/02665. The authors would like to give special thanks to Jacek Gładecki and Eliza Grajner-Rudaś for their help during field investigations. The authors would also like to thank the editor and three anonymous reviewers for their useful comments, which helped improving the manuscript.

References

Arias, M., Brown, M., and Sansalone, J. (2013). “Characterization of storm water–suspended sediments and phosphorus in an urban catchment in Florida.” J. Environ. Eng., 277–288.

Abstract

Introduction

Data and Methods

Catchment, Detention Pond, and Gauge Stations

Recorded Rainfall–Runoff–Sediment Events

Suspended Sediment Outflow Model for a Low-Volume Reservoir

Flow Continuity Equation

Suspended Sediment Continuity Equation

Model Calibration: Efficiency of Reconstructing Pond Outflow

Model Cross Validation: Efficiency of Predicting Pond Effluent Concentration

Results

Reconstruction of Recorded Flood Events

Sediment Decay Coefficient versus Detention Time

Efficiency of Predicting Pond Effluent Concentration

Discussion

Conclusions

Notation

Acknowledgments

References

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