Urban Stormwater and Sewerage Modelling: An Approach for Peak Runoff and Volume Assessment

In this study, an integrated approach for runoff estimation using the storm water management model (SWMM) was applied to undertake a stormwater and sewerage modelling in urban setting. The main objectives of the research and this manuscript include overload detection of sewer systems during extreme rainfall events with SWMM and to model and predict the relationship between precipitation parameters and overflooding of sewer collection system that includes emergency ponds to relieve flow from pump stations. The study takes into account monitored concurrent extreme rainfall event data and peak wet weather flows observed at outfall of collection system entering a wastewater treatment plant draining the urban centre. In the study SWMM was modified and adapted for the Tati and Ntshe confluence rivers draining the urban centre of Francistown in Northern Botswana. Landuse, soil, geological, drainage and sewerage network and imperviousness data sets were acquired and developed in GIS database. The runoff coefficient is found to range between 0.12 and 0.24 in the studied catchments. The calibrated model was able to predict the observed outputs with reasonable accuracy for calibration datasets of two peak flood events of 2016-Jan 12 and 2017-Feb 16 and verification flood events of 2016-Feb 05 and 2017-Feb 26. For six watersheds that drain the study area considered with a seventh entire collection system catchment area, we have evaluated the model performance using different criteria. We have found that correlation coefficients range from 0.539 to 0.813 and NSE ranges from 40.9% to 89.0%, and RSR ranges from 0.330 to 0.812 for the calibration


Introduction
In order to effectively manage and control the nuisance of frequent flooding during rainy seasons, designing an efficient stormwater drainage system in urban settlements is a frequent challenge for engineers and urban planners. The present case study deals with calibration and validation of a SWMM model for providing a solution to stormwater management problems in an urbanized area with scarce observed data. Urbanization creates infrastructure problems and large modifications in the environment. One of these challenges is the increase in urban runoff, causing or exacerbating the urban disasters generated by the floods. Furthermore, accelerated urbanization in different parts of the world has changed urban underlying surface, and the impervious proportion of areas has increased, resulting in lots of serious urban water problems [1]. High urbanization compounded with global climate change has also been the cause for increase in the frequency of extreme rainstorms [2]. Prudent management of urban collection systems is required to achieve sustainability in the water management and effective risk mitigation for urban settlements as illustrated in recent literature including [3] [4] [5] [6] [7].
In the late 1990s, as a best management practice, low impact development (LID) as a new concept was used in order to solve stormwater problems [8]. LIDs could control runoff from the source through infiltration, filtration, evapotranspiration and other natural hydrological processes, aiming to the reduction of runoff quantity and pollution, and the protection of the receiving water, which is different from traditional stormwater management [7].
In this study, evaluation of responses from urban watersheds is used as great interest for the urbanization flooding and modelling study in urban collection system. Various even-based hydrologic models are used to simulate rainfall-runoff processes in urban areas. Among these models, the Storm Water Management Model (SWMM) is a standard tool used widely. The present study was carried out to evaluate the use of the SWMM model on small sub catchments in an urban environment in a semi-arid setting. The focus was on the events calibration and on the understanding of the parameters involved in the simulation through a sensitivity analysis of them, based on observed field data from flow and rainfall monitoring.
Thus, the objectives of this research were to: 1) determine recommended model evaluation techniques (statistical and graphical); 2) review reported ranges of values that control rainfall-runoff processes and corresponding model perfor-Journal of Water Resource and Protection mance ratings; 3) establish guidelines for consistent model evaluation ratings; and 4) research on the relationship between precipitation parameters and sewer system overflooding. All of these objectives focus on simulation of urban runoff collection system in terms of flood hydrographs, volumes and runoff coefficient under data scarce conditions.
The study objectives were achieved with a thorough review of relevant literature on model application and recommended model evaluation methods between the observed and model-simulated results. In order to qualitatively evaluate results interactive visualization of hydrographs was also used to determine if the observed and simulated hydrographs match in terms of flood peaks and time of occurrence of peaks, volumes, etc. Three quantitative criteria were further recommended for model evaluation and determine model performance namely: the Nash-Sutcliffe efficiency (NSE), and ratio of the root mean square error to the standard deviation of measured data (RSR) and the Pearson's correlation coefficient (r). The following model evaluation performance ratings were established for each recommended statistic. In general, model simulation can be judged as satisfactory if r > 0.5, NSE > 50% and RSR < 0.70, constituent-specific performance ratings were determined based on uncertainty of measured data.
Additional considerations related to model evaluation guidelines are also discussed. These considerations include: single-event simulation, quality and quantity of measured data, model calibration procedure, evaluation time step, and project scope and magnitude.
A case study illustrating the application of the model evaluation guidelines is also provided. Discrete event-based urban rainfall-runoff quantity models have been applied such as in Moriasi et al., [9], Zaghloul [10] and Williams [11]. The models illustrated in Williams [11] are those which are widely used by federal agencies including the Rational Method; TR-20, used by the U.S. Soil Conservation Service (SCS); HEC-1, used by the U.S. Army Corps of Engineers (USACE); Urban Flood Hydrograph Synthesis Model (G824), used by the USGS; SWMM, developed for the U.S. Environmental Protection Agency (EPA); and MINICAT, used by the National Weather Service, River Forecast Center (RFC). The models were calibrated for peak discharge on the recorded floods, and all except the Rational Method were calibrated for runoff volume. In the continuous modelling of stormwater hydraulics and quality, SWMM model was applied for the calibration and verification processes of urban areas as noted recently including Patil et al. [12] and Cambez et al. [13].
Models for low impact urban stormwater drainage are applied across different urban development and catchment treatment settings [14]. These include impact  [29] is available that will help perform advanced analysis and visualizations of model data.

Description of Existing Urban Runoff Collection System
Description of existing urban runoff and sewage collection system is summarized in terms of the sub-drainage characteristics shown in Table 1 and illustrated in Figure 1. The collection system of the study area, the City of Francistown, is divided into six sub-basins forming the current and future service areas. These basins are named according to prominent geographic or landmarks which have evolved over years of a structured urban plan. Basin characteristics of the study sub-catchment areas are also shown in Table 1. The total area within the urban drainage area is 3982 hectares.
There are nearly 342,000 and 13,000 linear meter of gravity and pumping sewer pipes, respectively. The sewer network is served with more than 25 pumping stations. These sewer lines still in service range in size from 160 to  systems, which is a common problem in the study area.

Field Investigations
A variety of field investigations were performed. Every individual impervious surface was checked to estimate its hydraulic properties, including connectivity.
The pavement material of every sub-catchment was observed. The pavement material and physical connectivity of every sidewalk and driveway were also investigated carefully. The fluviometric and pluviometric data used in the simulations were obtained from monitoring stations inside the studied sub-catchments. Wet weather flows from the drainage area was used to obtain peak wet weather flow data by deducting the average dry weather flow.
Using a volumetric fit of 24-hr monitored peak runoff, the UH method was Journal of Water Resource and Protection used to determine the corresponding hourly hydrographs from the peak daily records. The subarea runoff hydrographs were also calculated by taking into account of the respective areas, imperviousness and soil infiltration parameters.
These were used as maximum indicative flow rates and corresponding dates of maximum rainfall data were collected and analysed to derive hourly rainfall intensities that will be input to SWMM.

Rainfall and Storm Events
The rainfall data available at daily steps were used to produce hourly rainfall intensities based on a regional approach presented in [30]. Some of the rainfall events were selected and classified in groups; according to the peak wet weather runoff generated which were then discretized and used as inputs for the model calibration and validation.
The mean annual rainfall in Francistown is 442 mm. The rainy season is from November to March and the dry period is between April and September. May to August is the coldest season with average minimum daily temperature reaching 5˚C and hottest season is between October and January where mean maximum temperature reaches above 30˚C.
The maximum rainfall value of 1hr duration, the maximum 1hr rainfall in a year is considered. For maximum values of 2-hr to 24-hr rainfall duration, the maximum rainfall in a year is considered. The total duration of this rainfall event  Table 2. These dates coincide with the maximum wet weather flow recorded in the drainage area and these concurrent records were used for further modelling evaluations. Table 3 shows the corresponding rainfall intensities for various durations for the considered rainfall events.

Soil Characteristics and Infiltration Parameters
Infiltration is often accounts for the largest portion of rainfall losses over pervious areas. Theoretically, infiltration is governed by the Richards equation [31] which requires that the relationship between soil permeability and pore water tension as a function of soil moisture content be known. In this study, the Horton's

Effect of Different Rainfall on Peak Runoff from SWMM Model
Rainfall intensities for various durations are used as main inputs to the SWMM model. Figure 2 shows hourly distribution for two peak rainfall events in the study area employed for model calibration vis-à-vis event 1-12 Jan 2016 and event 2-16 Jan 2017. System response of the existing drainage network for the two maximum rainfall events used for calibration is shown in Figure 3.
For sub-catchment S1 to S6 and the entire system catchment S7, the variation of runoff for corresponding rainfall is simulated by considering various events data. The runoff hydrographs are illustrated as presented in Figure 4 and Figure   5. The maximum peak runoff is 2.81 m 3 /s from sub-catchment 3 (S3) or Gerald and the lowest peak runoff is 0.74 m 3 /s from sub-catchment 6 (S6) or Madzibalori.
The magnitude of these maximum and minimum runoff peaks is in proportion to the relative catchment areas of the sub-catchments in the collection system.
The hydrograph of runoff from the individual contributing sub-catchments of the collection system are presented in Figure 6, and summarized in Table 4. It Journal of Water Resource and Protection can be noted that runoff is limited to less than 12 hours in most of the watersheds due to small time of concentration and short travel time in the smaller sized water sheds of the collection system.
The inflow and outflow represent the total runoff generated from contributing sub-catchments of the collection system while the outflow is the total routed runoff hydrograph in the outfall of the entire system. The flooding hydrograph  represents that direct runoff component resulting from the corresponding storm event. The total hourly runoff peaks resulting from the particular storm event is shown in Figure 3.
Spearman's correlation coefficient, r, a dimensionless quantity is used to determine the degree of linear correlation between two data sets defined by Equation (1) below. The Spearman Coefficient, r, can take a value between +1 to −1 where, value of +1 means a perfect association of rank.
( ) where n is number of data points of the two variables, and d i = difference in ranks of the "ith" element.

( )
The model performance criteria, root-mean square ratio (RSR) or ratio of the root mean square error to the standard deviation of measured data is calculated as, The Pearson correlation coefficient, r is also used as model performance and assessment criteria. The coefficient of determination R 2 is defined as the squared value of the coefficient of correlation r.

Calibration and Validation
Initial evaluation of results of SWMM model simulation were applied for the storm events and comparisons made with the monitored runoff of the wet weather flow data for the collection system. Wet weather flows from the drainage area flooding into the city's wastewater treatment plant was used to obtain peak wet weather flow data by deducting the average dry weather flow. Using a volumetric fit of 24-hr monitored peak runoff, the UH method was used to determine the corresponding hourly hydrographs from the peak daily records. The subarea runoff hydrographs were also calculated by taking into account of the respective areas, imperviousness and soil infiltration parameters.
In the calibration process, some observations could be made. Simplified discretizations would lead to the runoff peak greater than in detailed discretizations. In order to convert daily runoff from monitored data into hourly hydrograph ordinates, the triangular UH was used to transform the effective observed runoff to the outlet of each catchment. The peak runoff (Q p ) from is estimated from a watershed area A in (km 2 ) is given by Equation (5): with the discharge Q expressed as a ratio to the peak discharge Q p , and the abscissa is (t/T p ), which is the time t expressed as a ratio of the time to peak, T p .
The tabulations of the coordinates of the SCS dimensionless unit hydrograph are widely available in hydrologic literature for use in developing a synthetic unit hydrograph. This procedure was applied to determine the hourly realizations of Q hydrograph ordinates. Journal of Water Resource and Protection The proportional values of imperviousness and soil infiltration parameters of each sub-catchment were used in the initial evaluation of simulated outputs along with graphical visualization of hydrographs of the observed and SWMM-simulated runoff. The initial sets of outputs were runoff coefficient, total infiltration and total evaporation as shown in Table 5 and Table 6. These variables are related to the degree of imperviousness, land use and infiltration parameters of the existing soil types. Parameters were adjusted until reasonable match between the observed and simulated discharge hydrographs in terms of volumes, runoff peak and mean runoff is achieved. This was found to be useful as initial evaluation and visualization of hydrograph plots were made by interactively plotting SWMM outputs and observed hydrograph with a prudent adjustment of the landuse and soil infiltration parameters.
Initial analysis of results for the calibration and verification in terms of runoff coefficient, infiltration and evaporation are summarized in Table 5 and Table 6, With the procedure adopted to calibrate the events, a set of parameter combinations that led to the best fit between the observed and the simulated hydrographs was obtained for each rainfall event based model efficiency criteria namely, the Pearson correlation coefficient (r), the Nash-Sutcliffe efficiency (NSE), root-mean square ratio (RSR) including runoff peak values and volumes from the SWMM model against observed quantities. Table 7 and Table 8 show runoff volume, peak runoff and mean runoff of calibration dataset and validation data set, respectively. Whereas, Table 9 shows calibration results of SWMM model efficiency using Pearson correlation coefficient (r), Nash-Sutcliffe efficiency (NSE) and RSR calculated based on Equations (1), (2) and (4), respectively. The corresponding model performance indicators for validation data set are shown in Table 10.
Computed r values closer to 1 mean better simulation efficiency. In general, for the study area. Even though a mix of underestimation and overestimation in the hydrographs is prevalent, though insignificant, in most parts of the hydrograph is evident in terms of the 75%, 50% and 25% quantile flow regimes as presented in Table 11 and Table 12.

Parameter Sensitivity Analysis
Parameter sensitivity analysis was conducted on the events with the best results from the calibration exercise. The analysis was used to evaluate the main para-Journal of Water Resource and Protection meters that control the peak and volume of runoff. Starting from the set of parameters that led to the best calibrations per sub-basin (sub catchment), one parameter was varied at a time in fixed percentage increments, whose results were tabulated and compared.
Parameter sensitivity analysis was conducted on the events with the best results from the calibration exercise and the sensitivity analysis was performed by changing each parameter while keeping all others constant and observing the changes in model output. The analysis was used to evaluate the main parameters involved in terms of peak and volume of runoff. The percent changes in runoff volume and peak runoff were most sensitive to changes in imperviousness and storage. Changes in all other parameter were small and sometimes insignificant to runoff changes. A factor of 10% was used to vary the input parameters that control the runoff characteristics mainly the infiltration and surface roughness and land use factors, and the resulting runoff characteristics including total depth of runoff, volume of runoff and runoff coefficient, which were used to compute the impact on the model performance criteria, namely, the Pearson correlation coefficient (r), the Nash-Sutcliffe efficiency (NSE), root-mean square ratio (RSR). The simulated runoff characteristics in the output of the system conceptualization of SWMM that are compared to those determined from the real-world measurements of monitored data. Figure 7 shows the percentage change in simulated SWIMM runoff volume, total depth and runoff coefficient for percentage changes of infiltration and catchment parameters. In Figure 7, the infiltration parameters considered are the maximum or initial infiltration capacity (f0) in mm/hr, the minimum or equilibrium infiltration capacity (fc) in mm/hr and the decay coefficient (k) in hr-1 and catchment characteristics considered are imperviousness, slope and Manning's n of pervious area. From Figure 7 it can be said that generally increases in values of infiltration parameters results in decreases in runoff and vice versa. It can be seen from Figure 7 that increases in imperviousness also showed increases in runoff and vise versa. It can be deduced also that 10% -20% increases in pervious area n coefficient would result in decreases up to 20% of volume and runoff coefficient, and up to 10% of runoff depth.
Runoff characteristics for watersheds for calibration and validation datasets are presented in Table 11 and Table 12.
There is some but fairly distributed variation in the minimum and maximum values in all the watersheds of the study area. Besides the peak runoff, the descending runoff magnitudes of 75, 50 and 25 percent quantile runoff magnitudes (Q75, Q50 and Q25) are indicated. On the same table, the deviation of these quantiles of the observed runoff and those of the SWMM model simulated values are shown.
The changes in these quantities are in general between ±10% indicating reasonable matching of the hydrographs, even though there are few cases where deviations go beyond this range. There is generally higher range in the change of Journal of Water Resource and Protection lower runoff quantiles Q25 compared to Q50 and Q75.
The one-hr runoff simulated with SWMM in comparison with the observed runoff is presented in Table 13. In the calibration process, some observations could be made. In simplified discretizations of time steps, the runoff peak is greater than in detailed discretizations as noted in similar studies [10]. Reduction in time was noted in simplified discretization with an average value. It is possible to conclude that in natural river beds, when the water level grows until   [34]. Table   14 shows the performance of SWMM in terms of evaluating flow velocities in receiving channels. As the impervious cover increases or rainfall intensity increases in future, the peak discharge may exceed the design capacity of existing channel in sub catchment 4 and 6, where flow velocity is already high. To control the runoff on these sub catchments, there must be measures in future that can reduce the runoff such as introduction of continuous permeable pavements or infiltration trenches to improve infiltration.

Conclusions
Results of SWMM model runoff hydrographs from calibrated datasets and calibration datasets compared to observed hydrographs from the collection system are comparable. The runoff coefficient is found to range between 0. 12 (2).
The results obtained using the Pearson's correlation coefficient and the SWMM model software is almost equal to the observed values. As shown in Figure 8, Figure 8. Simulated runoff from SWMM and mean of observed runoff from discretization using UH method for Event 1: 12 Jan 2016. Journal of Water Resource and Protection the correlation coefficient is close to 0.9 where all the runoff values fall almost along the 45 degree line. The result of six sub-catchments, it can be said that existing drainage system is adequate for existing conditions. However, the runoff will change for critical storms other than the ones used in the current simulation events used in model calibration and verification. Comparison between mean simulated runoff and observed runoff from discretization using for various subcatchments of the same event is also shown in Figure 9.
This study can be used as a basis for infiltration and inflow (I/I) reduction analysis in urban sewerage systems. The study highlights on need for collection system configuration, flow monitoring data, and a The calibrated SWMM model can be considered to evaluate predicted storm runoff/ total wet weather flows from extreme rainfall storm events in the study area, while the available data as part of flow monitoring plan can be used to further assess wet weather flow to the City's wastewater treatment plant from individual basins and to quantify infiltration and inflow (I/I). Subsequently, this approach can be used to evaluate various management practices of reducing excess runoff in storm drainage systems as well as infiltration and inflow (I/I) reduction in sewer systems to alleviate excessive flows to wastewater treatment facilities [35].
Various excess storm runoff reductions in urban areas using infrastructural and nature based solutions are required to achieve sustainability in the sustainable water management and effective risk mitigation for urban settlements as discussed in [3]. Low impact development (LID) as a new conception was proposed in order to solve urban stormwater problem since the 1990s [36]. LID measures are also used as a means to control runoff from the source through infiltration, filtration, evapotranspiration and other natural hydrological processes, aiming to the reduction of runoff quantity and pollution, and the protection of the receiving water, which is different from traditional stormwater management [7].
As part of urban planning and development concept, the concept of LID has been developed to include the concept of Sponge city e.g. [7] [37]. Other concepts have also evolved such as Sustainable Urban Water Management (SUWM) [38]; Water Sensitivity Urban Design (WSUD) [39]; Sustainable Urban Drainage System (SUDS) [40] [41] and urban storm water quality and sediment management [42].