Development of probability distributions for urban ...

HYDROLOGICAL PROCESSES Hydrol. Process. (2013) Published online in Wiley Online Library (wileyonlinelibrary.com) DOI: 10.1002/hyp.10009

Development of probability distributions for urban hydrologic model parameters and a Monte Carlo analysis of model sensitivity James Knighton,1* Eric White,1 Edward Lennon1 and Rajesh Rajan2 1

Philadelphia Water Department, 1101 Market Street, Philadelphia, PA, 19107, USA 2 CDM Smith, 1500 JFK, Philadelphia, PA, 19102, USA

Abstract: This paper proposes an approach to estimating the uncertainty related to EPA Storm Water Management Model model parameters, percentage routed (PR) and saturated hydraulic conductivity (Ksat), which are used to calculate stormwater runoff volumes. The methodology proposed in this paper addresses uncertainty through the development of probability distributions for urban hydrologic parameters through extensive calibration to observed flow data in the Philadelphia collection system. The established probability distributions are then applied to the Philadelphia Southeast district model through a Monte Carlo approach to estimate the uncertainty in prediction of combined sewer overflow volumes as related to hydrologic model parameter estimation. Understanding urban hydrology is critical to defining urban water resource problems. A variety of land use types within Philadelphia coupled with a history of cut and fill have resulted in a patchwork of urban fill and native soils. The complexity of urban hydrology can make model parameter estimation and defining model uncertainty a difficult task. The development of probability distributions for hydrologic parameters applied through Monte Carlo simulations provided a significant improvement in estimating model uncertainty over traditional model sensitivity analysis. Copyright © 2013 John Wiley & Sons, Ltd. KEY WORDS

urban hydrology; model uncertainty; Monte Carlo; SWMM; hydraulic conductivity; Philadelphia

Received 23 April 2013; Accepted 9 August 2013

INTRODUCTION Understanding urban hydrology is critical to understanding urban water resource issues. An attempt to define the runoff response to precipitation is a common first step in approaching a variety of urban water issues such as flood protection, public health and environmental protection (Fletcher et al., 2013). Furthermore, designing and evaluating engineering solutions or control measures require an accurate definition of the hydrologic conditions and processes. It is often difficult to identify and quantify processes driving urban hydrology (Willemsand Berlamont, 1999; Willems, 2008; Ampe et al., 2012; Fletcher et al., 2013; Verbeiren et al., 2013). The more accurate the predictions of a hydrologic model, the better equipped an agency or organization is to spend available resources in an efficient manner (Maidment, 1993). Urban hydrology within Philadelphia

A description of native soil formations for Philadelphia County is given by the US Department of Agriculture *Correspondence to: James Knighton, Office of Watersheds, Philadelphia Water Department, 1101 Market Street, 4th Floor, Philadelphia, PA 19107, USA. E-mail: [email protected]

Copyright © 2013 John Wiley & Sons, Ltd.

(USDA, 1975). Within Philadelphia, however, a variety of land use types coupled with a history of cut and fill have resulted in a patchwork of urban fill and native soils (Levine, 2013). Where native soils do exist, engineering of the landscape has resulted in varying levels of soil compaction. Though updated soil maps of Philadelphia exist, the majority of the area served by combined sewers is listed as urban fill (MuSym code: Ur) (NRCS, 2013). Infiltration tests performed across Philadelphia in support of green stormwater infrastructure design have returned a wide range of saturated hydraulic conductivity (Ksat) values with no significant correlation between infiltration rate and location (Philadelphia Water Department unpublished data). Stormwater flow paths in urban areas can be equally unpredictable. Plumbing code for Philadelphia specifies that rooftop leaders be connected to the combined sewer system. Exceptions to the code exist, however, as flood prone houses fitted with a backflow prevention device are required to disconnect roof leaders from the combined sewer system (City of Philadelphia, 2005). Additionally, the Philadelphia Water Department runs a pilot program which encourages residential properties to disconnect roof leaders into stormwater controls such as rain gardens and

J. KNIGHTON ET AL.

downspout planters (Philadelphia Water Department, 2012). Flow paths can be further complicated by temporarily blocked inlets and imprecise delineation of street grading. An attempt to generalize the complicated stormwater flow paths of a given section of Philadelphia in a simplified hydrologic model is therefore accompanied by significant uncertainty. Model uncertainty analysis typically focuses on error in primary data sources (precipitation and flow monitoring), error in model parameter estimation and error introduced through simplification of physical processes (Willems and Berlamont, 1999; James, 2003; Harmel et al., 2006; Freni et al., 2009). Recent advances in model validation have seen attempts to quantify error introduced through model parameter estimation on projects with little or no data (Freni et al., 2009; Fu et al., 2011). These attempts to quantify uncertainty are valid approaches; however, they only represent cases where data collection efforts are not given significant attention or resources. Modeling of combined sewer overflows

Policy guiding control of combined sewer overflows (CSO) is outlined by the National Pollutant Discharge Elimination System (EPA, 1994). In response to this permitting program, the Long Term Control Plan Update for Philadelphia outlines a plan to reduce combined sewer overflow (CSO) volumes. As part of the Long Term Control Plan Update, Philadelphia has developed EPA Storm Water Management Model (SWMM) hydraulic and hydrologic models of each of the city’s three combined sewer districts to estimate CSO volumes and test the effects of CSO control measures. SWMM is a hydrologic rainfall–runoff model coupled with a hydraulic model for routing runoff through simulated collection systems. SWMM models are typically employed in urban water resources engineering projects. A common challenge in SWMM modeling of CSO systems is estimation of the rainfall–runoff relationship within the hydrologic model (EPA, 2010). The initial uncertainty analysis focusing on hydrologic model parameter estimation resulted in a wide range of potential CSO volumes (Philadelphia Water Department, 2011). The Philadelphia Water Department maintains a flow monitoring program in support of the Long Term Control Plan Update and department wide capital planning initiatives. Flow monitors are deployed at strategic locations throughout the area served by combined sewer system to obtain data on depth of flow and mean flow velocity. Hydrologic and hydraulic model parameters of the area served by combined sewer system and the collector systems are then refined to match observed flows. Through flow monitoring, hydrologic parameter values can be estimated relatively accurately for a subset of the area served by Copyright © 2013 John Wiley & Sons, Ltd.

combined sewer system. Through a deployment of 50 flow monitors covering 38.6 km2 within the combined sewer service area and a model validation exercise, a dataset of hydraulic and hydrologic model parameters has been established. This paper outlines a heuristic approach to quantifying model sensitivity. The final validation parameters from the flow monitoring deployment were assembled into probability distributions for urban hydrologic model parameter values for Philadelphia. The resulting probability distributions were then applied across the Southeast drainage district through Monte Carlo simulation in order to define model uncertainty. METHODOLOGY EPA SWMM model structure

The basic hydrologic representations of EPA SWMM (build 5.0.022) are model elements termed subcatchments. A subcatchment is a hydrologic unit that drains to a single point. The extent to which a study area is divided into subcatchments is user defined. Within a subcatchment, hydrologic parameters such as total area, average land slope, depression storage, surface roughness and width (a routing parameter) can be defined. Subcatchments can be further subdivided into pervious and impervious subareas. Several methods of internal routing between pervious and impervious areas are supported (EPA, 2010). Existing Philadelphia Water Department datasets allow for a fairly accurate estimate of average land slope, Manning’s roughness, gross percent impervious cover and depression storage (Philadelphia Water Department unpublished data). In this modeling exercise, the PERVIOUS routing method was selected based on the judgment of the authors that this simplification would most closely represent potential flow paths within Philadelphia. In the PERVIOUS routing method, a portion of the impervious area, represented as the model parameter percentage routed (PR), is routed over the entire length of the pervious area (EPA, 2010). The Green–Ampt method was selected to simulate infiltration. Green–Ampt infiltration requires estimates of Ksat, suction head (S) and initial moisture deficit (IMD). Of these unknown parameters, the infiltration volume is most sensitive to Ksat. Model validation therefore focused on Ksat. Appropriate values for S and IMD were chosen to match each validated Ksat value (Maidment, 1993). Flow monitoring and precipitation data

Flow data from 50 flow monitor deployments from 2007 through 2012 were evaluated for validation of runoff parameters. The flow monitoring deployment covered 38.6 km2 (23%) of the total combined sewered area (Figure 1). Hach Sigma Model 910 Systems (Hach, Hydrol. Process. (2013)

MONTE CARLO ANALYSIS OF URBAN HYDROLOGIC PARAMETERS

Rainfall data measured at rain gages only represents conditions at the location of the gage; therefore, assumptions were made about precipitation between rain gages. Rainfall data was distributed to each subcatchment using the inverse distance squared weighting method. The inverse distance weighting method may misrepresent events with significant spatial variation in precipitation (Maidment, 1993). In the validation dataset, spatially varied events were identified and removed due to nonrepresentative rainfall measurements. Snow events and rain events influenced by snow melt were removed from consideration as the SWMM snow melt routine is not currently employed by the Philadelphia combined sewer overflow model (EPA, 2013). Figure 1. Combined sewered area with monitored subcatchments

Model validation

Loveland, Colorado) were used to record flow depth and velocity data within the combined sewer at 15 min increments. Pipe shapes were confirmed in the field to ensure that proper depth to area relationships were used in the calculation of flow rates. Installation of flow monitoring equipment and field verifications were performed by CSL Services, Inc. (Pennsauken Township, New Jersey). Quality assurance and quality control (QAQC) of flow monitoring data was performed by the Philadelphia Water Department. Hydraulic limitations within the collection system prevent monitoring of the entire simulated area, forcing assumptions to be made about unmonitored areas. The suitability of a site for flow monitoring was assessed prior to installation of each flow meter. Site conditions such as depth of flow, velocity of flow, turbulence, grit buildup, pipe size and profile, evidence of surcharging, access and safety conditions were evaluated for each flow monitoring location. Flow monitors were installed in sites that met the criteria for suitable flow monitoring. Flow monitoring data was validated with handheld readings of depth and velocity every 2 weeks throughout the deployment. Following collection of flow monitoring data, a visual QAQC procedure was used to eliminate periods of questionable or erroneous flow monitoring data. Hydrograph separation was performed visually with the EPA Sanitary Sewer Overflow Analysis and Planning Toolbox (EPA, 2013). The resulting wet weather hydrographs were compared with precipitation estimates as a final quality control of the observed flow data. Precipitation was measured by the Philadelphia Water Department rain gage network of 24 gages. Rain gages used were tipping bucket Met-One Instruments Inc. (Grant Pass, Oregon) model 385. The rain gage network was field verified once a month with a test volume of water. A redundant rain gage deployment occurred on a rotating schedule as a second verification of rain gage accuracy. Copyright © 2013 John Wiley & Sons, Ltd.

The hydrologic model validation procedures were similar to those described in Long Term Control Plan Update Supplemental Documentation Volume 4: Hydrologic and Hydraulic Modeling (Philadelphia Water Department, 2011). The hydrologic parameter Ksat has been frequently identified as a sensitive parameter for calibration of SWMM runoff volumes (Tsihrintzis and Hamid, 1998; Zaghloul and Keifa, 2001; PWD, 2011). Through a sensitivity analysis of model parameters, PR was identified as a sensitive parameter for the Philadelphia collection system model (PWD, 2011). PR and Ksat were manually adjusted for all subcatchments contributing to a flow monitor until the SWMM model matched observed event total volumes (Figures 2 and 3). Total subcatchment runoff volume was not sensitive to subcatchment width or depression storage. These parameters were therefore not included in the sensitivity analysis. Wet weather events were sorted into two categories, events generating only impervious area runoff and events generating pervious runoff. Events generating only impervious runoff were isolated to determine the appropriate

Figure 2. Simulated flows, observed flows and rainfall at F04-000180 on 3/10/2010 and 3/11/2010

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would occur in areas of lower gross impervious cover due to less development and, therefore, less overall compaction of the soils. These results suggest that while urban areas may have similar land uses, pathways for stormwater are complex (e.g. disconnected downspouts, blocked inlets, etc.) and somewhat unpredictable.

Figure 3. Simulated versus observed event volume totals for F04-000180

PR value for the subcatchment. Mid-range to large storms generating runoff from pervious areas were used to define values for soil parameters. Best fit PR and Ksat values were determined by the slope of the best fit line through scatter of observed versus simulated event volumes, while maximizing the coefficient of determination (Figure 3). Seasonal variation in hydrologic processes can result in seasonal model parameter values (Maidment, 1993). For the purposes of estimating annual average combined sewer overflow volumes, a single averaged hydrologic parameter value was estimated for each location. Sitespecific conditions and observed rainfall patterns limited the collection of flow monitoring data at some locations, which resulted in a varied number of validation events per each monitoring site. Validated parameter values. Once the model was validated at all 50 monitoring sites, distributions were developed for both PR and Ksat. The final validated parameter values at each site are provided in Table I. Percent routed (PR): Final validation values for PR from 50 validation sites were compiled. The resulting distribution of final validated PR values has a mean of 34% with a standard deviation of 11.7% and passes tests for normality (Figure 5). (D’Agostino test for normality; HO: distribution is normal, HA: distribution is not normal; Χ2 = 1.2719, p value = 0.5294; skewness = 0.9085, p value = 0.3636; kurtosis = 0.6683, p value = 0.504 as calculated with fBasics v2160.85 in R 3.0.0 (R Core Team, 2012)). Contrary to initial hypothesis, no correlation was found between PR values and gross impervious cover or Ksat of the monitored subcatchments (Table I). It was assumed that higher percentage gross impervious cover would result in lower percentage of impervious surfaces routed to pervious surfaces due to the decrease in opportunity for routing. Additionally, it was assumed that higher infiltration rates Copyright © 2013 John Wiley & Sons, Ltd.

Infiltration (soils): Final validated Ksat values from 37 sites were used in developing a cumulative frequency distribution (Figure 6). Results from 13 flow monitors were not used to define soil parameters due to a lack of significant events occurring through the deployment that resulted in runoff from pervious areas. The median Ksat value from the distribution was 1.27 cm/h. The 5th and 95th percentiles for the observed CDF of the validated parameter value are 0.52 and 5.97 cm/h, respectively. Discussion of error in model parameter estimation

The final validated models did not provide an exact match of the observed flow monitoring data. A review of the R2 values for best fit linear regression through simulated versus observed event volumes suggests that observed precipitation and the validated SWMM model alone cannot explain all variance in observed flows (Table I). The potential sources of error in flow predictions include errors in precipitation measurement and distribution, observed flow measurement, model parameter estimates, spatial resolution of the model, representation of the pipe network and simplification of hydraulic and hydrologic processes (Willems and Berlamont, 1999; James, 2003; Freni et al., 2009). In an attempt to quantify model uncertainty, procedures followed were similar to those described by Willems and Berlamont (1999). All potential sources of validation data error and model output error are estimated, followed by attempts to identify the sources of the model error. Due to the large areas uncovered by rain gages in the study area, spatially varied events could have potentially produced errors in rainfall estimates. All spatially varied rain events were identified and removed from the validation analysis. Additionally, all snow events, and events influenced by snowmelt were removed as the model snowmelt routine is currently not employed. It is assumed that these efforts have reduced rainfall error to the error documented by the manufacturer. Currently, the rain gage network is calibrated and maintained such that the maximum allowable gage error at the time of field verification is ±5% based on manufacturing documentation and QAQC procedures. This is most likely an underestimate of the error introduced through the precipitation data. The maximum error in acceptable flow monitoring data is estimated as ±15% based on dye testing of flow monitoring equipment and field procedures followed by CSL Services Inc. (Pennsauken Township, New Jersey). Hydrol. Process. (2013)


Table I. Flow monitoring deployments and associated final validated parameters 1R-squared of linear regression of monitored versus modeled total event volume (Figure 3) Manhole ID C06-000010 C11-000110 C12-000020 C17-000202 C17-000810 C17-003360 C24-000010 C37-000010 D02-000020 D03-000010 D05-000150 D05-001112 D05-001187 D18-000010 D22-000120 D25-000150 D38-000690 D40-000010 D41-000010 D54-000070 D54-000150 D61-000015 D63-000035 D63-000080 D65-000010 D67-000010 F04-000180 F07-000010 F11-000130 F21-009745 F23-000010 S05-004405 S20-000070 S42-000130 S42-000530 S42A-000795 S45-001110 S50-001600 S50-002920 T01-000010 T03-000010 T06-000075 T08-000270 T13-000015 T14-000345 T14-000490 T14-001300 T14-013940 T14-014030 T14-029300

Drainage area (km2)

Percent gross impervious

n events

Percent routed (PR)

Ksat (cm/h)

0.39 0.55 0.23 0.82 0.64 0.78 0.13 0.05 1.28 0.45 1.37 1.82 0.98 0.72 0.31 1.40 0.77 0.18 0.20 0.37 0.77 0.10 1.48 0.69 1.05 0.52 1.05 0.33 0.69 1.47 0.21 0.04 0.36 0.30 0.45 0.30 0.25 0.29 0.57 0.66 0.40 0.22 3.91 0.47 3.39 1.23 0.99 0.56 2.06 0.36

72% 70% 75% 79% 77% 78% 51% 55% 76% 57% 73% 68% 67% 77% 83% 73% 74% 74% 78% 89% 68% 74% 83% 82% 78% 86% 59% 82% 63% 64% 65% 77% 75% 85% 79% 85% 62% 72% 62% 62% 74% 69% 62% 75% 53% 46% 75% 55% 53% 51%

21 46 28 49 26 47 23 23 14 15 54 49 48 26 19 41 37 18 34 28 41 15 47 13 61 29 78 17 47 74 17 27 60 71 29 19 62 56 36 55 49 30 98 18 13 58 33 39 53 29

50% 43% 45% 25% 40% 35% 35% 20% 35% 20% 10% 10% 45% 30% 65% 31% 40% 20% 45% 38% 30% 30% 30% 50% 20% 30% 40% 28% 35% 30% 40% 45% 30% 30% 40% 50% 40% 55% 50% 20% 40% 10% 50% 20% 40% 40% 35% 40% 40% 50%

3.99 1.30 5.21 0.53 0.53 1.57 0.99 0.25 0.30 1.32 1.32 1.32 5.97 1.32 5.28 2.54 1.32 0.69 1.42 6.81 0.69 2.18 2.72 2.18 0.69 0.69 4.32 1.22 5.97 1.32 1.22 0.79 2.03 4.78 2.72 2.72 0.51 2.72 1.37 1.32 4.95 0.30 1.88 5.97 2.54 2.54 0.41 2.54 0.89 2.54

Rigorous QAQC procedures discussed above are assumed to have limited erroneous flow measurements from being included in the analysis. The error in model estimates of runoff volume (95% prediction interval) is estimated between ±5% and ±30%. Assuming ±5% and ±15% error is introduced through Copyright © 2013 John Wiley & Sons, Ltd.

R2

1

0.99 0.91 0.67 0.92 0.98 0.93 0.99 0.98 0.83 0.82 0.96 0.98 0.94 0.99 0.94 0.99 0.86 0.95 0.92 0.97 0.94 0.99 0.97 0.99 0.97 0.88 0.97 0.98 0.98 0.90 0.99 0.82 0.88 0.89 0.97 0.97 0.88 0.96 0.97 0.68 0.97 0.78 0.86 0.91 0.79 0.76 0.98 0.97 0.94 0.84

precipitation and flow monitoring data, respectively, model error introduces at most ±10% in the estimate of event runoff volumes. Error in the estimation of hydrologic parameters is assumed to be negligible. The probability distributions developed for the Ksat and PR during model calibration were utilized to examine the Hydrol. Process. (2013)

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impact of these two parameters (along with appropriate values for S and IMD) on model uncertainty ranges, assuming that all other error sources remained constant. Monte Carlo distribution of validation parameters

Flow monitoring and validation efforts yielded probability distributions for hydrologic parameter values (Figures 4 and 6). The sensitivity of the model runoff to estimated runoff parameters was tested through a Monte Carlo simulation (Thorndal and Willems, 2008; Alvarez, 2009; Martin and Ayesa, 2010; Fu et al., 2011). Monte Carlo methods take a heuristic approach to parameter estimation and test the sensitivity of model outputs to parameter uncertainty. The PR and Ksat parameters for each subcatchment were treated as random variables defined by the above empirical probability distributions. A series of Python 2.7 (http:// www.python.org/) scripts were written to generate Monte Carlo simulations of the SWMM combined sewer service area model with randomly assigned Ksat and PR values.

Figure 4. Cumulative frequency distribution for final validated PR values for Philadelphia

Ksat values were randomly chosen from a discrete uniform distribution defined by the established cumulative frequency distribution (Figure 6). IMD and S values were generated from a lookup table for typical soil parameters as defined in Maidment (1993). PR values were sampled from a continuous normal distribution (μ = 34%, σ = 11.7%). PR values sampled outside of the possible range (100%) were sampled repeatedly until a realistic value was reached (Figure 4). An R 2.15.2 (R Core Team, 2012) script was written to compile the results of the simulated system wide overflow volumes and summarize outputs. Typical hydrologic year model runs to estimate annual CSO volume

As a case study, the effects of model parameter uncertainty on the CSO volumes of the Philadelphia Southeast combined sewer drainage district SWMM model were assessed. The sensitivity analysis was performed on the model estimate of district wide CSO volume as a result of typical year precipitation. The Southeast drainage district combined sewer model is composed of 301 subcatchments, 736 nodes and 829 links (Philadelphia Water Department, 2011). The typical hydrologic year is a modified version of observed 2005 precipitation for the Philadelphia region. The dataset was originally developed as part of the Philadelphia Water Department Long Term Control Plan Update (PWD, 2011) as a method of establishing a benchmark for systematic changes to CSO volumes. The resulting CSO volume is anticipated to be representative of the long term average annual CSO volume. As the dataset is artificial, no uncertainty is assigned to primary precipitation data used to predict annual average CSO volumes.

RESULTS Combined sewer overflow uncertainty

A series of simulations involving 10, 50, 100 and 1000 model runs were performed to determine the computational

Figure 5. Q–Q test for normality of final PR values (μ = 34%, σ = 11.7%) Copyright © 2013 John Wiley & Sons, Ltd.

Figure 6. CDF of validated Ksat values for Philadelphia



demand required to generate a meaningful estimate of sensitivity of system wide CSO volume to unknown hydrologic parameters. Uncertainty associated with PR and Ksat (along with associated S and IMD values) generates an uncertainty range of ±7.4% of the average annual CSO volume (95% prediction interval, 1000 Monte Carlo simulations). The resulting distribution of combined sewer overflow volumes was positively skewed, towards higher overflow volumes (G = 0.0891) (Figure 10). Computational demand

All models randomly generated by the Python script were divided across two, high-end, personal computers, each separating the model runs into five parallel processes. The total run time for these 1000 simulations in ten parallel processes was 260 h. This was a substantial increase from the original modeling approach, which relied on three model runs developed from low, median and high parameter values; the previous approach was run in parallel in approximately 2 h.

parameters. Datasets defining urban hydrology are not widely available and are largely dependent on local conditions. The development of probability distributions for model parameters marks a significant improvement over value ranges available in literature (Chow et al., 1988; Maidment, 1993; Chin, 2006; EPA, 2010). The Monte Carlo approach to estimating uncertainty in total overflow volume attributable to model parameter estimation reduced the overall model uncertainty considerably. A test of 1000 simulations generated a cumulative frequency distribution of overflow volumes (Figure 10). Results were normalized to total median overflow volume to represent uncertainty as a percentage. The results suggest

DISCUSSION Monte Carlo approach to defining uncertainty

Common approaches of estimating model uncertainty follow standard probability theory. Model components are typically assessed individually, with model sensitivity determined for each parameter (Lei and Schilling, 1994; Guo and Adams, 1998; Harmel et al., 2006). A sensitivity analysis of individual model parameters, while a useful tool, can neglect cancelling or amplifying effects of changes to multiple model parameters together (Fu et al., 2011). This classic approach to estimating model uncertainty was used with earlier iterations of the Philadelphia Southeast drainage district combined sewer system model. Through this case study, uncertainty related to several model parameters are considered at once. The parameters driving the model processes studied (PR, or percentage of total impervious subcatchment area routed over the total pervious area and soil parameters defining infiltration rates) can both have an amplifying or cancelling effect on the other’s influence on CSO volume. The fate of impervious runoff routed over pervious areas is largely controlled by the infiltration rate of the pervious areas. Extreme low infiltration rates may cancel the effects of modifying the PR parameter. Similarly, extremely large infiltration rates may amplify the effect of percent routed on total runoff volume. The effect of one variable cannot be uncoupled from the other. This problem therefore lends itself more to a Monte Carlo analysis of model sensitivity (Fu et al., 2011). The flow monitoring deployment allowed improvement of probability distributions for urban hydrologic model Copyright © 2013 John Wiley & Sons, Ltd.

Figure 7. CDF of total district CSO volumes represented as percentage difference from median for ten model permutations

Figure 8. CDF of total district CSO volumes represented as percentage difference from median for 50 model permutations


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Computational demand and model output resolution

While all runs involving different numbers of Monte Carlo simulations were adequate estimators of mean system overflow volume, the prediction interval of model estimate of total system overflow decreased as the number of simulations increased (Figures 7–10). A marked decrease in the prediction interval width occurred as the number of simulations was increased from 10 to 50. Above 50 simulations, refinement of the 95% prediction interval was modest. While Monte Carlo simulation is powerful in that it can more accurately quantify hydrologic uncertainty among coupled hydrologic parameters, it significantly increased the computational demand required to generate a model-based prediction. Figure 9. CDF of total district CSO volumes represented as percentage difference from median for 100 model permutations

Figure 10. CDF of total district CSO volumes represented as percentage difference from median for 1000 model permutations

that hydrologic model parameter uncertainty is ±7.4% of the total overflow volume (95% confidence interval). The resulting positive skew of combined sewer overflow volumes indicates that more uncertainty lies in larger overflow volumes. Combined sewer overflows are the result of hydrologic processes overwhelming the hydraulic capacity of the collection system. For smaller events, though some uncertainty in runoff may exist, the hydraulic capacity of the system prevents combined sewer overflows. Smaller events will therefore have less variability as the runoff volume has no effect on overflow volume. As runoff increases, the number of events causing overflows increases. The observed positive skew in combined sewer overflows is likely the result of increases in volume and frequency of overflows. Copyright © 2013 John Wiley & Sons, Ltd.

CONCLUSIONS 1. Probability distributions for SWMM model parameters PR and Ksat were developed for Philadelphia through flow monitoring and model calibration. Further flow monitoring will be performed to better define the established parameter value distributions. 2. Monte Carlo methods were applied to simulation to estimate model sensitivity to hydrologic parameters PR, and Ksat, S and IMD as applied to the Green–Ampt method of infiltration. The Monte Carlo methods provided a marked improvement over classic uncertainty analysis employed previously. This research suggests that through an improved methodology for estimating model uncertainty, monitoring a subset (23%) of the total simulated area may be adequate for estimating district wide CSO volumes. 3. A minimum of 50 Monte Carlo simulations was required to develop a reasonable estimate of CSO volume uncertainty with respect to hydrologic parameters. Additional simulations provide a more refined estimate of uncertainty; however, the computational demand increases.

ACKNOWLEDGEMENTS

This work was performed within the Philadelphia Water Department Office of Watersheds H&H Modeling Group. We thank Gary Martens and Dr. Jim Smullen (CDM Smith) for modeling advice. We thank Matt Plourde (Sci-Tek Consultants, Inc.) for R program development and advice.

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