Global analysis of sensitivity of bioretention cell design elements to hydrologic performance

Yan-wei SUN, Xiao-mei WEI*, Christine A. POMEROY

1. College of Water Resources and Architectural Engineering, Northwest A & F University,Yangling 712100, P. R. China

2. Department of Civil and Environmental Engineering, University of Utah, Salt Lake City, UT 84112, USA

1 Introduction

Low impact development (LID)is a site design strategy with the goal of maintaining or replicating the predevelopment hydrologic regime through the creation of a functionally equivalent hydrologic landscape (PGC 1999). It is receiving more and more attention in America and Europe (Dietz 2007). Bioretention cells, also known as bio-infiltration facilities or rain gardens, are a form of urban storm water LID that reduces runoff quantity and improves water quality in a natural and aesthetically pleasing manner, and is becoming one of the most popular LIDs (Davis et al. 2009). As a consequence, the design elements of bioretention cells are becoming one of the fundamental theoretical issues. Several studies have been conducted to examine impacts of different media depths and media mixtures on the performances of bioretention cells in water quality and water quantity, both from laboratory tests and field evaluation (Brown and Hunt III 2010; Dietz 2005; Hsieh and Davis 2005).However, most of the current studies are based on single rainfall events; information about impacts of different design elements on the bioretention cell performance from a long-term continual simulation or field researches is still limited.

Sensitivity analysis evaluates how the variations in the model output correspond to variations in model parameters (Cloke et al. 2008). Saltelli et al. (2000)classified the sensitivity techniques into two groups: local sensitivity analysis (LSA)methods and global sensitivity analysis (GSA)methods. The LSA techniques examine the local response of the output(s)by varying one input parameter at a time, with other parameters unchanged. GSA provides several advantages over LSA, such as “rigorously mapping the space of possible model predictions, decomposing the total uncertainty due to the various model input parameters, and understanding the influence of the different sensitivities of each model input parameter” (Cloke et al. 2008). Therefore, GSA has been more widely used than LSA. Many GSA techniques are currently available, including the Morris method (Brockmann and Morgenroth 2007), the Fourier amplitude sensitivity test (FAST)(McRae et al. 1982), and Sobol’s method (Sobol 2001). The Morris method has been applied widely for devising an efficient way of sampling a parameter space to provide the minimal number of model evaluations required.

In this study, the Morris method was used to examine the impacts of bioretention cell design elements on hydrologic performance and to identify relatively important design elements based on GSA. The results are important in offering the guidelines for bioretention cell design.

2 Design issues of bioretention

Bioretention is a terrestrial-based, water quality- and water quantity-controlled practice using the chemical, biological, and physical properties of plants, microbes, and soils for removal of pollutants from storm water runoff. Some of the processes that may take place in a bioretention cell include sedimentation, adsorption, filtration, volatilization, ion exchange,decomposition, phytoremediation, bioremediation, and storage (PGC 1999). Fig. 1 is a diagram of a typical bioretention cell structure. Design of a typical bioretention cell needs to consider the mulch layer, ponding area, planting soil, underdrain, gravel layer, and native soil.

(1)The mulch layer plays a vitally important role in the overall bioretention design.Shredded (or chipped)hardwood is used to retain moisture and minimize erosion. This layer serves to prevent erosion and to protect the soil from excessive drying.

(2)The ponding area provides surface storage of the storm water runoff and evaporation of a portion of the runoff. Ponding design depths have been kept to a minimum to reduce hydraulic overload of in situ soils/soil medium and to maximize the ratio of the surface area to bioretention cell depth, where space allows. The maximum ponding depth has been set to 15.2 cm in order to draw any pooled water within 48 h.

(3)The planting soil is the region that provides the water and nutrients for the plants to sustain growth and promote the decomposition of organic material and adsorption and bonding of heavy metals. It is also referred to as soil media or the root zone. The soil is critical to the success of any bioretention cell. From a practical standpoint, it must drain appropriately while having the necessary organic elements to sustain the plant community and biological processes.It can either drain very fast or slow. Prince George’s County (PGC 2007)recommends a filter media or planting soil depth of 76 cm to 122 cm.

Fig. 1 Diagram of a typical bioretention cell

(4)Underdrain is optional and if geotechnical tests show that the in situ soils meet or exceed the medium soil guidelines for infiltration rates, no underdrain will be required. The role of an underdrain in the bioretention cell is to ensure proper drainage for the plants and to ensure the occurrence of proper infiltration rates. The underdrain system also provides a discharge point that precludes the need for extensive geotechnical investigation.

(5)The gravel layer is used for the storage of infiltrated water. Gravel bed materials are sometimes used to protect an underdrain pipe in order to reduce clogging potential.

(6)Native soil is the soil under gravels. The main restriction for use of soil in bioretention cells is that the soil must have an infiltration rate sufficient to draw down any pooled water within 48 h after a storm event. This requires that the soil infiltration rate should exceed 1.32 cm/h.

The size and saturated infiltration rate of the design elements of a typical bioretention cell are summarized in Table 1 based on the recommendation of PGC (2007). The ideal area for bioretention cells should be no larger than 0.12 km2and the slope should be less than 5% for best performance.

Table 1 Summary of bioretention cell design elements

3 Study area

The study area is located within Lenexa City, Kansas, USA. It is a parking lot located between W 87th Street and Pflumm Road. The study area is approximately 0.017 km2and is a highly developed urban area with an imperviousness of 86%. The study area’s location is shown in Fig. 2.

Fig. 2 Location of study area

The study area was selected because it has the independent drainage area for building bioretention cells recommended by PGC (2007), and allows for easy access to data, including precipitation and evaporation data, topographic data, and soil data. The study area is also one sub-catchment in the EPA-SWMM (environmental protection agency storm water management model)in Report of the Detention Study in City of Lenexa (Pomeroy et al. 2008).Therefore, time and effort in initial model development and calibration have been greatly saved. The EPA-SWMM (short for SWMM)is a dynamic rainfall-runoff simulation model used for single event or long-term continuous simulation of runoff quantity and quality from primarily urban areas. It was used in this study (Rossman 2009). The hourly rainfall data from 1974 were selected for the simulation based on the analysis showing that there was no data gap in 1974 and the total rainfall depth was 91.75 cm, only 1.65 cm less than the 50-year average annual record, and the data were used to represent the rainfall tendency in this area.

4 Methodology

4.1 Model approach

As far as hydrologic performance of bioretention cells is concerned, the monitoring approach is most widely used, but it is limited by the long time period of monitoring data and the effort to obtain the data (Asleson et al. 2009). Especially for the area where best management practices will be established, the only way to predict the performance is by simulation using realistic models.

SWMM was used in this study based on the existing model for the runoff simulation. An hourly time step was set to obtain the data format required by RECARGA. The RECARGA model is an event- or continuous-based model that simulates the hydrologic function of bioretention cells based on MATLAB (Atchison and Severson 2004). The model continuously simulates the water movement throughout the bioretention cell (ponding area, planting soil,and underdrain), records the soil moisture and volume of water in each water budget term(infiltration, recharge, overflow, underdrain flow, evapotranspiration, etc.)at each time step,and summarizes the results. The new version 2.1 of RECARGA allows the users to input the runoff time series generated by the external model. In this study, SWMM and RECARGA were used for the hydrologic performance analysis of bioretention cells. First, SWMM was applied to generate the runoff time series of different samples with different surface areas and the generated runoff time series were edited afterwards in the format demanded by RECARGA. The REARGA model was run for different bioretention samples to obtain the outflow time series for further performances analysis. Finally, the Morris method was used to obtain the elements most sensitive to the performance metrics.

4.2 Selection, ranges, and sample generation of evaluated design elements

Currently, most research on design elements focuses on bioretention cell sizing, planting soil depth, and media. Sizing is the first step towards a construction activity or simulation of bioretention cells. In the study, the bioretention cell surface area was selected for the sensitivity analysis. Palhegyi (2010)reviewed the eight currently popular sizing methods and concluded that the surface area varied by 5% to 24% of the whole drainage area, based on which the bioretention cell surface area within 5% to 24% of the study area was selected.Since the planting soil layer is the main zone where chemical and biological processes take place and the major cost of construction occurs, both the components and depth have been studied for performance improvement and cost reduction. In this study, the depth of planting soil varying from 76 cm to 122 cm and the saturated infiltration rate varying from 1.32 cm/h to 6.12 cm/h recommended by PGC (2007)were selected for the sensitivity analysis. Design of the gravel layer has not been studied much because it has no effect on the water quality treatment. However, as a storage layer, it is capable of storing runoff temporarily and promoting the infiltration to the groundwater. The water movement in the gravel layer is fast enough that the infiltration rate can be ignored and, therefore, only the depth of the gravel layer was selected to conduct the sensitivity analysis. It varied within the range of 15.25 cm and 30.5 cm recommended by PGC. Native soil is an important design element because it determines the volume and rate of runoff infiltrating into groundwater. The saturated infiltration rate of native soil in the study area is a constant. However, four types of native soil,sand, loamy sand, sandy loam, and loam, which are approved by PGC for bioretention cells,were selected for the simulation. In this study, the saturated infiltration rates ranged from 1.32 cm/h to 21.01cm/h. Since underdrain is only necessary when the saturated infiltration rate of native soil is less than 1.32 cm/h and the native soil classes approved by PGC are applied,the sensitivity analysis of underdrain sizes was only conducted when the saturated infiltration rate of native soil was less than 1.32 cm/h, generating the two groups of samples shown in Table 2 and Table 3, respectively.

Table 2 Ranges of selected design elements of bioretention cells without underdrain

With limited knowledge of parameter distribution of the selected design elements, the uniform distributions were applied. The Morris method was used to generate samples for the two groups individually and generated 30 samples for the bioretention cell without underdrain and 35 samples for the bioretention cell with underdrain.

Table 3 Ranges of selected design elements of bioretention cells with underdrain

4.3 Hydrologic performance metrics of bioretention cell

By controlling the regional surface runoff and infiltration to the groundwater, the bioretention cell tries to mimic the pre-developed runoff regimes (PGC 1999). The hydrologic performances of bioretention cells were facilitated with consideration of four metrics: the overflow ratio, groundwater recharge ratio, ponding time, and runoff coefficients. The overflow ratio refers to the ratio of the overflow untreated by bioretention cells to the total surface runoff of the study area. The groundwater recharge ratio, the ratio of the runoff infiltrated to the groundwater to the total inflow, together with the overflow ratio, represents the infiltration performances. Ponding time is the time when there is water in the ponding zone,and it is another metric to represent the infiltration performances and depression storage. The runoff coefficient, which is the ratio of the corresponding runoff volume (in unit of cm)to the total rainfall event volume (in unit of cm)is a metric that examines the overall hydrologic performances of bioretention cells, since the typical site’s runoff coefficient can be maintained at the pre-developed (under natural and undisturbed conditions)level by compensating for the loss of abstraction (interception, infiltration, and depression storage)through both site planning and design considerations. To obtain direct knowledge of impacts of bioretention cells on the runoff coefficient, another metric, Rc, was introduced in this study to represent the ratio of the pre-developed runoff coefficient (natural and undisturbed runoff coefficient)to the bioretention cell-controlled runoff coefficient, which is expressed in Eq. (1):

where Rcis a metric representing the performances of bioretention cells on runoff coefficients, Cpreis the runoff coefficient under pre-developed conditions, and CBiois the runoff coefficient after bioretention cells are controlled. The closer Rcis to 1, the closer CBiois to Cpre, indicating a better hydrologic performance.

4.4 Morris method

The Morris method is a typical GSA technology. It is useful for carrying out screening analyses with a limited number of model runs without going through a full sampling-based uncertainty analysis and was therefore used in this study. The Morris method has been well documented and the following is a brief review.

The Morris method is based on the elementary effect for each input parameter. Assuming that a k-dimensional vector of input parameters X1,X2,… ,Xkis given, and the range of each input variable is divided into p levels, the elementary effect di(x)of the input parameter Xifor a given value x=(x1,… ,xk)is de fi ned as follows:

where Δ∈ {1 (p - 1), 2 (p - 1), … ,1- 1 (p -1)}is fi xed, and y denotes a model response. In simple words, the elementary effect di(x)is a difference between the model response at the new value of parameter Xi, either increased or decreased by Δ, and the model response at the old value of this parameter.

By randomly sampling different x values from the input space, the distribution of elementary effects Fiassociated with the ith parameter is obtained. The sensitivity measuresμ and σ are, respectively, the estimates of the mean and standard deviations of the distribution. The mean μ?of the distribution of absolute values of the elementary effects was used to deal with the effects of different signs. Generally, μ?estimates the overall effect of the parameters on the output and σ estimates the ensemble of the parameter effects(Salacinska et al. 2010). It can be seen that μ?is in fact similar to total sensitivity and,therefore, was used in this study.

5 Results and discussion

5.1 Sensitivity analysis results for bioretention cell design elements without underdrain

The SWMM and RECARGA models were run for each sample to obtain the corresponding runoff series and the metrics discussed above. The average and standard deviations of overflow ratio, groundwater recharge ratio, CBio, and Rcare shown in Table 4.The average overflow was 8.55% and the average groundwater recharge ratio was 89.16%,indicating a prominent runoff control performance. The average Rcwas 1.02, which is close to the runoff coefficient under pre-developed conditions, indicating a prominent overall hydrologic performance when the saturated infiltration rate of native soil is larger than 1.32 cm/h. Because the ponding time was less than 48 h for all the samples, the ponding time is not discussed for this group.

Table 4 Average and standard deviations of hydrologic performance metrics for bioretention cell design elements without underdrain

The global sensitivity analysis was conducted for the hydrologic metrics generated by the samples. Table 5 shows the results of the global sensitivity μ?of the design elements to the hydrologic performance metrics of the overflow ratio, groundwater recharge ratio, CBio, and. The ranks from 1 to 5 represent the sensitivity degrees, where 1 indicates most sensitive and 5 indicates least sensitive.

Table 5 Sensitivity analysis results for bioretention cell design elements without underdrain

As shown in Table 5, when the saturated infiltration rate of native soil is greater than 1.32 cm/h, Afis the most sensitive element to all hydrologic performance metrics. This can be explained because the larger the bioretention cell’s size, the smaller the area’s imperviousness. Besides Af, Kpand Knare the other two most sensitive elements to the overflow ratio, CBio, and Rc. For the groundwater recharge ratio, Dpis more sensitive than. The reason is that when the saturated infiltration rate in the samples is larger than the inflow rate to the bioretention cell, water infiltrates rapidly enough for all the samples. To conclude, when the saturated infiltration rate of native soil is large enough and there is no underdrain, Afand Kpare the two most sensitive design elements, while Dgis the least sensitive element to all the hydrologic performance metrics.

5.2 Sensitivity analysis results for bioretention cell design elements with underdrain

When the saturated infiltration rate of native soil is less than 1.32 cm/h, the bioretention cells must be installed with underdrain to guarantee the runoff drawdown time less than 48 h in order not to cause harm to the growth of plants and their aesthetic function. Two metrics,the maximum ponding time and the total ponding time, were added in the sensitivity analysis to examine the infiltration performances (Table 6).

Table 6 Average and standard deviations of hydrologic performance metrics for bioretention cell design elements with underdrain

As shown in Table 6, the average maximum ponding time and the average total ponding time were 52.66 h and 186.29 h, respectively. The average overflow ratio increased and the average groundwater recharge ratio decreased compared with the values in the scenario when the saturated infiltration rate of native soil was greater than 1.32 cm/h, indicating a diminishing in hydrologic performance when the native soil is less than 1.32 cm/h. There were obvious increases in standard deviation of the overflow ratio, the groundwater recharge ratio,, and Rc, which means that the values of these metrics vary greatly and the changes of the design element values are more sensitive to the hydrologic metrics for this group. The sensitivity analysis was conducted and the results are presented in Table 7.

Table 7 Sensitivity analysis results for bioretention cell design elements with underdrain

As shown in Table 7, the sensitivities of the design elements rank differently for different hydrologic performance metrics. For the maximum ponding time, Knand Duare the two most sensitive elements. For the total ponding time, Afand Knare the two most sensitive design elements. For the overflow ratio, the groundwater recharge ratio, CBio, and Rc, Afis the most sensitive design element, followed by Kn. Dgis least sensitive to all the performance metrics.

Comparing the results with Table 5, we find that Afis the most sensitive design element to all performance metrics except the maximum ponding time, and Dgis the least sensitive element whether the bioretention cell is installed with underdrain or not. For the bioretention cells installed with underdrain, sensitivity of Knand Kpto the hydrologic metrics of the overflow ratio, the groundwater recharge ratio, CBio, and Rcindicated great differences from the results of bioretention cells without underdrain. For the bioretention cells installed with underdrain, Knis the second most sensitive design element to the hydrologic metrics except the maximum ponding time while Kpis the second sensitive element for the metrics without consideration of the ponding time for the bioretention cells without underdrain.This is because when the saturated infiltration rate of native soil is large enough, the water can infiltrate rapidly and the saturated infiltration rate of planting soil is the main element limiting the water flowing into the bioretention cells. However, when the saturated infiltration rate of native soil is lower than the saturated infiltration rate of planting soil, it becomes the main element limiting the infiltration and the most sensitive element rather than saturated infiltration rate of planting soil. In addition, for bioretention cells with underdrain, Du,followed by Kn, is another sensitive design element for most hydrologic metrics. Ranks ofand Dgmake no great differences for bioretention cells with and without underdrain.

Comparing the sensitivity analysis results of each design element of Af,Dp, and Dgto all the performance metrics except the ponding time with and without underdrain, we find that the sensitivity values in Table 7 are larger than those in Table 5, which confirms that the design elements are more sensitive when the saturated infiltration rate of native soil is lower.This is because the overflow ratio, the groundwater recharge ratio, CBio, and Rcrepresent bioretention cells infiltration performances, which are determined by the rate of inflow to the bioretention cell and water movement in it. Planting soil acts like a sponge and will release flow in the form of overflow as soon as it reaches its maximum capacity, which is determined by both the inflow runoff rate and the saturated infiltration rate of native soil. When the saturated infiltration rate of native soil is low enough, the planting soil will reach its maximum capacity quickly, which allows more overflow and less infiltration, and, consequently, greater variation and sensitivity values for the hydrologic metrics of the overflow ratio, groundwater recharge ratio, CBio, and Rc. For the urban area, changes in the magnitude, frequency, and duration of runoff are greater after urbanization when the saturated infiltration rate of native soil is low, which makes it necessary to construct the LIDs or other BMPs. Therefore, when the saturated infiltration rate of native soil is low, it is meaningful to discuss the sensitive design elements in order to aid design goals and reduce the cost of bioretention cells.

However, it is hard to conduct sensitivity analysis using the monitoring data from real constructed bioretention cells with different design elements and the same regional runoff regime. Currently, there are few studies on the relative importance of bioretention design elements on hydrologic performances, and most relevant studies are conducted on the laboratory scale and through the model approach. The results presented in this study were also obtained through a rigid model approach, which will offer theoretical background to guide engineering practice. However, constructed examples may be needed to prove the model results.

6 Conclusions

SWMM was used in this study to generate the runoff series for each bioretention cell sample and RECARGA was used to simulate and calculate the hydrologic performance metrics. Based on the performance metrics, the Morris method was conducted with two groups of design elements without underdrain and with underdrain, respectively. The following conclusions were drawn based on the study:

(1)The bioretention cell surface area is the most sensitive design element to most of the hydrologic performance metrics for both groups without underdrain and with underdrain,while the depth of the gravel is the least sensitive design element.

(2)When the bioretention cell is not installed with underdrain, the saturated infiltration rate of planting soil and the saturated infiltration rate of native soil are the two most sensitive design elements besides the bioretention cell surface area.

(3)When the bioretention cell is installed with underdrain, the saturated infiltration rate of native soil and underdrain size are the two most sensitive design elements besides the bioretention cell surface area.

(4)The design elements with underdrain are more sensitive to the hydrologic performance metrics than those without underdrain.

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