Citation
Development of surface and sub-surface hydrologic model for storm water infiltration practices

Material Information

Title:
Development of surface and sub-surface hydrologic model for storm water infiltration practices
Creator:
Luu, Toan Manh ( author )
Place of Publication:
Denver, CO
Publisher:
University of Colorado Denver
Publication Date:
Language:
English
Physical Description:
1 electronic file (165 pages). : ;

Subjects

Subjects / Keywords:
Storm water retention basins ( lcsh )
Rain gardens ( lcsh )
Genre:
bibliography ( marcgt )
theses ( marcgt )
non-fiction ( marcgt )

Notes

Review:
Urban development results in increases of runoff rates and volumes. Since the early 1970's, storm water detention has been recommended as an effective means to reduce the peak flow generated from the extreme events. Through the years from 1990 to 2000, the renaissance of urban storm water management leads to a new era under the new concept of low-impact-development (lid). The LID approach is mainly developed to cope with the small frequent storm events. With both flood mitigation and LID approaches, an urban watershed's hydrologic regime can be preserved. Among many creative ideas for developing engineering LID devices, rain garden is the most popular storm water infiltrating facility designed for on-site runoff volume reduction and water quality enhancement. A rain garden consists of a surface storage basin and subsurface infiltrating media. The storage basin is designed to store the water quality capture volume (WQCV) while the subsurface infiltrating system is composed of two layers of filtering media. The upper layer is filled with sand-mix and the lower layer is formed with gravels. The drain time is the most important design parameter for rain garden's operation. A short drain time will lead to an inadequate residence time for sedimentation process and not delay the peak runoff flow while a long drain time will raise the risk to have the next storm event before the basin dries up. A new rain garden usually has a high infiltration capacity through the filtering layers therefore rain garden's drain time is short. Over years of service, the clogging effect in the filtering layers will slow down its infiltration rate or prolong its drain time. To improve the performance of a rain garden through its life cycle, it is recommended that a cap-orifice be installed at the outlet of the perforated underdrain pipe. The challenges in rain garden design include how to (1) select the design event to size the surface basin, how to (2) predict to the surface-subsurface flow through the filtering layers, and how to (3) adjust the cap-orifice to achieve the targeted flow release and drain time according to the stage of rain garden's life cycle. In this study, several probability models were evaluated to portray the distributions of event runoff depths generated from 30 to 40-year long-term one-hour continuous rainfall events recorded in 9 metropolitan areas in the US continent. It was confirmed that the log-normal distribution gives the overall best fitted curve that can be further used to select the water quality capture volume (WQCV) to size the rain garden's storage basin. WQCV is found to be related to the local statistics of event rainfall depths, watershed imperviousness, and statistics of event rainfall depths, watershed imperviousness, and targeted runoff treatment percentage. The optimal WQCV generated from the log-normal distribution for runoff event depths is able to treat 80 to 90 percent of runoff volume generated from the tributary watershed. This conclusion is close to the US Environmental Protection Agency's recommendation on 80 percent runoff capture and treatment for stormwater quality enhancement management. To predict the sub-surface flow movement, a diffusion-based sub-surface hydrologic model is developed to predict the water infiltrating process through the unsaturated and saturated sand-mix zones underneath a rain garden. The key factors for this numerical model are the soil initial moisture content and hydraulic conductivity which can be calibrated with field data. During the early years in a rain garden's service. The cap-orifice is used to regulate its flow release. For a given history is terms of field data, the numerical procedure developed in this study provides a quantifiable guidance on how to turn the cap-orifice up and down to satisfy the design condition. In coordination with the Urban Drainage and Flood Control District (UDFCD), Denver, Colorado, a prototype rain garden was built in the city of Lakewood, Colorado, as a test site. The proposed methods and models derived in this study were tested and calibrated by 4-year field data collected at the test site. This numerical procedure significantly improves the current subjective and empirical operations at UDFCD. It is expected that this software engineering and algorithm derived in this study for rain garden's operation will be further incorporated in to a remote automation process that can be operated in office to control a rain garden's operation from a distance.
Thesis:
Thesis (Ph.D.)--University of Colorado Denver. Civil engineering
Bibliography:
Includes bibliographic references.
System Details:
System requirements: Adobe Reader.
General Note:
Department of Civil Engineering
Statement of Responsibility:
by Toan Manh Luu.

Record Information

Source Institution:
|University of Colorado Denver
Holding Location:
|Auraria Library
Rights Management:
All applicable rights reserved by the source institution and holding location.
Resource Identifier:
913231182 ( OCLC )
ocn913231182

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DEVELOPMENT OF SURFACE AND SUB SURFACE HYDROLOGIC MODEL FOR STORM WATER INFILTRATION PRACTICES by T OAN MANH LUU B.S., Vietnam Water Resources University, 1995 M.S., University of Colorado Denver, 2006 A thesis submitted to the Faculty of the Graduate School of the University of Colorado in partial fulfillment of the requirements for the degree of Doctor of Philosophy Civil Engineering 201 5

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ii This thesis for the Doctor of Philosophy degree by Toan Manh Luu has been a pproved for the Civil Engineering Program b y David C. Mays, Chair James C. Y. Guo, Advisor Balaji Rajagopalan Zhiyong Jason Ren Indrani Pal April 21 2015

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iii Luu, Manh Toan (Ph.D., Civil Engineering ) Development of Surface and Sub surface Hydrologic Model for Stormwater Infiltration Practices Thesis directed by Professor James C. Guo. ABSTRACT Urban development results in increases of runoff rates and volumes. as an effective means to reduce the peak of flow generated from the extreme events. Through the years from 1990 to 2000, the rena issa nce of urban storm water management leads to a new era under the new concept of low impact development (LID). The LID approach is mainly developed to cope with the small, frequent storm even ts. With both flood mitigation and LID approaches, a n Among many creative ideas for developing engineering LID devices, r ain garden is the most popular storm water infiltrating facility designed for on site runoff volume reduction and water quality enhancement. A rain garden consists of a surface storage basin and subsurface infiltrating media. The storage basin is designed to store the water quality capt ure volume (WQCV) while the subsurface infiltrating system is composed of two layers of filtering media. The upper layer is filled with sand mix and the lower layer is formed with gravels. The drain time is the most important design parameter for rain gard time will lead to an inadequate residence time for sedimentation process and not delay the peak runoff flow while a long drain time will raise the risk to have the next storm event before the basin dries up. A new rain garden usually has a high

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iv infiltration capac ity through the filtering layer s therefore drain time is short Over years of service, the clogging effect in the filtering layers will slow down its infiltration rate or prolong its drain time To improve the performance of a rain garden through its life cycle, it is recommended that a cap orifice be installed at the outlet of the perforated underdrain pipe. The challenges in rain garden design include how to (1) select the design event to size the surfac e basin, how to (2) predict to the surface subsurface flow through the filtering layers, and how to (3) adjust the cap orifice to achieve the targeted flow release and drain time cycle. In this study, several probability model s were evaluated to portray the distributions of event runoff depths generated from 30 to 40 year long term one hr continuous rainfall event s recorded in 9 metropolitan areas in the US continent I t was confirmed that the log normal distri bution gives the overall best fitted curve that can be further used to select the water quality capture volume (WQCV) to size the WQCV is found to be related to the local statistics of event rainfall depths, watershed imperviou sness, and targeted runoff treatment percentage. The optimal WQCV generated from the log normal distribution for runoff event depths is able to treat 80 to 90% of runoff volume generated from the tributary watershed This conclusion is close to the US Envi and treatment for stormwater quality enhancement management.

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v To predict the sub surface flow movement, a diffusion based sub surface hydrologic model i s developed to predict the water infi ltrating process through the unsaturated and saturated sand mix zones underneath a rain garden. The key factors for t his numerical model are the soil initial moisture content and hydraulic conductivity which can be calibrated with field data. During the early years in a orifice is used to regulate its flow release. For a given history in terms of field data, the numerical procedure developed in this study provides a quantifiable guidance on how to turn the cap ori fice up and down to satisfy the design condition. In coordination with the Urban Drainage and Flood Control District (UDFCD) Denver, Colorado, a prototype rain garden was built in the City of L akewood Colorado as a test site. The proposed methods and mo dels derived in this study were tested and calibrated by 4 year field data collected at the test site This numerical procedure significantly improve s the current subjec tive and empirical operation s at UDFCD It is expected that this software engineering a nd algorithm derived in this study for incorporated in to a remote automation process that can be operated in office to from a distance. The form and content of this abstract are a pprov ed. I recommend its publication. Approved: James C. Y. Guo

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vi ACKNOWLEDG E MENT First, I would like to express my greatest appreciation to my adviser, Dr. James C. Y. Guo, who persistently supported and encouraged me to complete my research projects from the M.S. through Ph.D. st udies Since 2004, over a period of 10 years w orking with Dr. Guo was great experience for me not only to enhance my professional insights, but also to learn many as pects of personal and family life I would also like to th ank all members of my dissertation committee for their suggestions and comments on my studies I would like to thank the Civil Engineering Department for the fund ing support during my study. Thanks to Mr. Ken Mackenzie and his staffs from the U rban D rainage and Flood Control District, Denver, Colorado for providing a test field to collect data sets for rainfall, runoff, seepage flows for several years. Finally, I would lik e to thank my parents, brothers, sisters and friends for their constant support and encouragement I am grateful to my wife, Thuy Ngo for having patience and supporting me during all these years. I would also like to thank my two wonderful sons, Minh Luu and Huy Luu for inspiring me.

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vii TABLE OF CONTENTS Chapter 1. I ntroduction ................................ ................................ ................................ .... 1 1.1 Urbanization ................................ ................................ ................................ 1 1.2 Impacts of Urbanization on Stormwater ................................ ...................... 2 1.3 Development of Storm Water Management ................................ ................ 2 1.4 Objectives ................................ ................................ ................................ .... 9 2. W ater Quality Capture Volume for Storage Basin ................................ ....... 11 2.1 Introduction ................................ ................................ ................................ 11 2.2 Review of P revious Studies ................................ ................................ ....... 13 2.3 Surface Runoff Model Development ................................ .......................... 14 2.3.1 Model Codes ................................ ................................ ................................ .. 14 2.3.2 Analysis of Complete Rainfall Data Base ................................ ................. 14 2.3.2.1 Rainfall Data ................................ ................................ ................ 14 2.3.2.2 Event Separating by Inter Event Time ................................ ......... 19 2.3.3 Statistical Model for Rainfall Event Depths ................................ ............... 21 2.3.4 Lognormal Distribution for WQCV ................................ .............................. 31 2.4 Geometry of Water Quality Basin ................................ .............................. 34 2.5 Optimization Analysis for Runoff Volume Capture Rate ............................ 35 2.5.1 Introduction ................................ ................................ ................................ .... 35 2.5.2 Design Example ................................ ................................ ............................ 39 2.5.3 Co nclusion ................................ ................................ ................................ ..... 41 3. H ydrologic Model for Infiltrating Process ................................ ..................... 43 3.1 Introduction ................................ ................................ ................................ 43 3.2 Reviews of Previous Studies ................................ ................................ ..... 44 3.3 Governing Equation for Infiltrating Water Flow ................................ .......... 45 3.4 Procedure for Solving the Governing Equation ................................ ......... 51

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viii 3.5 Conclusion ................................ ................................ ................................ 54 4. Case Stu dy ................................ ................................ ................................ .. 55 4.1 Study Area ................................ ................................ ................................ 55 4.2 Field Data Collection ................................ ................................ ................. 59 4.2.1 Rainfall Data ................................ ................................ ................................ .. 59 4.2.2 Inflow Measurement ................................ ................................ ..................... 60 4.2.3 Outflow Measurement ................................ ................................ .................. 62 4.3 Calibrating the Model Parameters ................................ ............................. 63 4.3.1 SWMM Model for Surface Runoff Hydrograph ................................ ........ 63 4.3.2 Seepage Flows from Rain Garden ................................ ............................. 68 4.3.3 Conclusion ................................ ................................ ................................ ..... 72 4.4 Determining Drain Time for Rain Garden ................................ .................. 72 4.5 Cap Orifice Sizing Design ................................ ................................ ......... 77 4.5.1 Procedure for Determining the Diameter of Cap Orifice ........................ 77 4.5.2 Design Example ................................ ................................ ............................ 79 Cap Orifice Installation .......................... 80 5. C onclusions ................................ ................................ ................................ 83 5.1 Green Concept ................................ ................................ .......................... 83 5.2. Evaluation of Green Stormwater Management ................................ ......... 84 5.2.1 Detention Basin Sizing Stage Storage Relationship ................................ .. 85 5.2.2 Outlet Vault for Flow Release Control Stage Outflow Curve ..................... 87 5.2.3 Test on stormwater Green Management ................................ .................. 92 5. 3 Conclusion ................................ ................................ ................................ 95 REFERENCES ................................ ................................ ................................ ... 98 APPENDIX A. Some Other Rainfall Events Applied in the Case Study ............................ 102 B. The Surface and Sub Surface Numerical Model s ................................ ..... 106

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ix LIST OF TABLES T able 2.1 Summary of Rainfall Data Records ................................ ............................ 16 2.2 Original Hourly Rainfall Data of Denver City ................................ ............... 17 2.3 Input File for Surface Numerical Model ................................ ....................... 18 2.4 Statistics for Rainfall Events using MIT=6 hours ................................ ........ 21 2.5 AIC Value for Distribution of Rainfall Event Depth using MIT=6 hr ............. 26 2.6 AIC Value for Distribution of Rainfall Event Depth using MIT=12 hr ........... 26 2.7 AIC Value for Distribution of Rainfall Event Depth using MIT=24 hr ........... 27 2.8 The Values of K and RVCR for Drain Time=12 hr and Various Land Uses 38 2.9 The Values of K and RVCR for Drain Time=24 hr and Various Land Uses 38 2.10 Rainfall Statistics for Selected Locations ................................ .................. 39 2.11 for Drain Time=12 hr and 24 hr at Denver, CO 41 4.1 Rainfall Events Applied for Rain garden in the Study Area ......................... 59 4.2 Land Use Characteristics of the Study Area ................................ ............... 64 5 1 Stage Area Storage for Proposed Detention Basin ................................ .. 8 7 5.2 Stage Outflow for Detention Basin System ................................ ................ 90

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x LIST OF FIGURES F igure 1.1 Detention System with Infiltration Pool ................................ ......................... 4 1.2 Detention System with Perforated Plate for All Event Release Control ........ 4 1.3 A Rain Garden Built in Denver ................................ ................................ ...... 7 1.4 Layout of Rain Garden ................................ ................................ ................. 7 2.1 Micro minor major Cascading Flow Systems on Street .............................. 11 2.2 Locations of Rain Gauges (Source: Google.com) ................................ ...... 15 2.3 Rainfall Event Separation using MIT=12 Hours ................................ .......... 20 2.4 Boxplot and Rainfall Event Depth Distribution ................................ ............ 23 2.5 .............. 24 2.6 Various Models for Distribution of Rainfall Event Depths at Denver with MIT=12 hr ................................ ................................ ................................ ........... 25 2.7 Rainfall Event Depths for Houston, TX, using MIT=6 Hours ....................... 27 2.8 Rainfall Event Depths for San Francisco, CA, using MIT=6 Hours ............. 28 2.9 Rainfall Event Depths for Denver, CO, using MIT=12 Hours ...................... 28 2.10 Rainfall Event Depths for Boston, MA, using MIT=12 Hours .................... 29 2.11 Rainfall Event Depths for Phoenix, AZ, using MIT=24 Hours ................... 29 2.12 Rainfall Event Depths for Chicago, IL, using MIT=24 Hours ..................... 30 2.13 Rainfall Event Depths for Seattle, WA, using MIT=24 Hours .................... 30 2.14 Runoff Volume Capture Curve for MIT=12 hr at Denver, CO ................... 33 2.15 Runoff Volume Capture Curve for MIT=24 hr at Boston, MA ................... 34 2.16 Runoff Capture Curve for WQCV with C=0.5, Drain Time=12 hr at Denver, CO ................................ ................................ ................................ ...................... 35 3.1 Layout of Rain Garden ................................ ................................ ............... 44

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xi 3.2 Illustration of Flows through Filtering Layer in a rain garden System ......... 46 3.3 Soil Tension Moisture Characteristic Curve ( Scheffer 2002) ...................... 48 3.4 Sketch of Rain Garden ................................ ................................ ............... 49 3.5 Flowchart for Numerical Subsurface Model ................................ ................ 53 4.1 Location of Rain Garden at Lakewood, CO (Source: Google.com) ............ 56 4.2 Tributary Watershed to Rain Garden (Source: UDFCD) ............................. 57 4.3 Rain Garden before Growth (Source: UDFCD) ................................ .......... 57 4.4 The Rain Garden after Planting Vegetation (Source: UDFCD) ................... 58 4.5 The Rain Garden during Operation ................................ ............................ 58 4.6 A Rain Gauge at the Study Area ................................ ................................ 60 4.7 Inflow Station ................................ ................................ .............................. 61 4.8 V notch Weir Dimension for Inflow Measurement ................................ ....... 61 4.9 Outflow Station ................................ ................................ ........................... 62 4.10 V notch Weir Dimension for Outflow Measurement ................................ .. 63 4.11 SWMM for the Tributary Watershed ................................ ......................... 64 4.12 Computed and Observed Runoff Hydrograph for May 18, 2011 Event .... 65 4.13 Runoff Volume Intercepted at Rain Garden for May 18, 2011 Event ........ 66 4.14 Runoff Volume Intercepted at Rain Garden for July 09, 2012 Event ........ 66 4.15 Runoff Volume Intercepted at Rain Garden for September 22, 20 13 Event ................................ ................................ ................................ ........................... 67 4.16 Runoff Volume Intercepted at Rain Garden for July 08, 2014 Event ........ 67 4.17 Observed and Predicted Seepage Flows through Sand Layer in Rain Garden for May 18, 2011 Event ................................ ................................ .......... 69 4.18 Observed and Predicted Seepage Flows through Sand Layer in Rain Garden for July 09, 2012 Event ................................ ................................ .......... 70 4.19 Observed and Predicted Seepage Flows through Sand Layer in Rain Garden for September 22, 2013 Event ................................ ............................... 71

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xii 4.20 Observed and Predicted Seepage Flows through Sand Layer in Rain Garden for July 08, 2014 Event ................................ ................................ .......... 71 4.21 Observed and Predicted Seepage Flows through Rain Garden for July 9, 2012 Event ................................ ................................ ................................ ......... 74 4.22 Orifice Size for July 9, 2012 Event ................................ ................................ ................................ .................. 74 4.23 Observed and Predicted Seepage Flows through Rain Garden for September 22, 2013 Event ................................ ................................ ................. 75 4 .24 Orifice Size for September 22, 2013 Event ................................ ................................ ................................ ... 75 4.25 Observed and Predicted Seep age Flows through Rain Garden for July 08, 2014 Event ................................ ................................ ................................ ......... 76 4.26 Orifice Size for July 08, 2014 Event ................................ ................................ ................................ ......... 76 4.27 Adjustment using Valve for Seepage Flows ................................ ............. 81 5.1 SWMM Model Layout of Test Watershed ................................ ................... 8 4 5.2 Detention Volume Determined by Hydrograph Methods ............................ 86 5.3 Sketch of Flood Detention for 10 to 100 yr Events ................................ .... 8 6 5.4 Outlet for 100 yr Release Control for Case (A) .... 88 5.5 Outlet for Full Spectrum Release Control for Case (B) ............................... 88 5.6 Outfall Pipe and Culvert Hydraulics ................................ ............................ 89 5.7 Stage Outflow for 100 yr Flood Control ................................ ...................... 9 1 5. 8 Stage Outflow for 10 yr and Slow Release Control ................................ ... 9 2 5. 9 Outflows Release from Test Watershed for All Events .............................. 9 3 5. 10 Outflows Release from Test Watershed for 30 year Rainfall Data at Denver City ................................ ................................ ................................ ..................... 9 4 5. 11 Outflows Release from Test Watershed for More Frequent Events . 9 4

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1 1. I ntroduction 1.1 Urbanization W orld population has been increased quickly since the last half century In the year 1950, the population was around 2.6 billion people I n the 2013, the world population is almost 7.15 billion people and there will be around 8.9 billion people in the year 2050 (United State Census Bureau 2012) Over the time mo re and more people want to find a better life in the ci ties because the c ity is a center of industry, education, and politics. As a result, u rbanization has been expanded rapidly every year In the year of 1950 30% of world population lived in the cities N ow the city dweller is more than 50% and in the year 20 5 0 the urban people are expected to be around 61.8 % (UNHABITAT 2010). The growth rate of urbanization of America is even more rapid than any other country in the world. In the year 1950, 64 % of peopl e reside d in the cities (Bogue 1955) In 2010 80.7% people live d in the urban area (United State Census Bureau 2010). Colora do is one of state America with population of 5.03 million people and 86. 2 % of population were city dwellers in 2010 (United State Census Bureau 2010) There will be around 6.0 million people by 2020 and around 8.0 million people by 2040 (DeGroen 2012). The urban characteristics are high population density and rapid infrastructure development such as roads, houses, bui lding s The infrastructure development is a main reason in increas ing the impervious area in the urban places

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2 1.2 Impacts of Urbanization on Stormwater The rapid increase of the impervious area s in the cities due to urbanization adversely affect s rain water falling in the urban areas. Impervious area s prevent the stormwater from infiltrating into groundwater system and increase the runoff volume and peak flow on surface area The more paved area is the more r unoff volume peak flow and pollutant will be. The runoff volume is 3.8 times larger and the peak flow is 1.6 times higher when comparing the watershed before development with 5% impervious area and after development with 95% impervious area (Guo 2006) Pollutants such as dirt, chemicals from stre ets and construction areas are easily cleane d up from the surface by stormwater runoff during rainfall events and they are quickly conveyed to receiving water in the downstream area. Consequently, urbanization ha s induced more complicated problems that are associated with storm water for receiving water in the downstream area such as water (EPA 1983). 1.3 Development of S torm W ater M anagement To reduce the negative effects of stormwater runoff on urban area many storm water management practices have been developed t o satisfy the requirement of people and society development. Before the year of 1970, urban drainage practices were to focus on how to collect and transport flood f lows out of streets and urban areas, using gutters, storm drains, culverts and channel s. This practice resulted in a significant increase in storm runoff peak flows, volumes, pollutants and groundwater depletion ( EPA 1983; Guo 2006; Athayde

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3 1976) During t popular means to reduce peak flows for extreme events such as 10 year to 100 year events. Stormwater detention does not reduce the total runoff volume but gradually releases the stored volume at a high flow rate over a long drain time As a result, sto rmwater detention practices induce more frequent high flows to natural streams and cause significant deterioration s in water quality and aquatic habitats ( EPA 1983; Booth and Jackson 1997 ) Duri ng the 1980 s, the EPA Nation wide Urban R unoff Program ( EPA 1983) had initiated a public concern about urban water environmental preservation. As a result, under the mandate of the Federal Clean Water Act (USWDCM 2001) flood control systems and stormwater management practices must be designed and operated to reduce the runoff volumes using infiltrating practices and to release the runoff flows not exceeding the pre development condition During best management practices (BMP) s hifted its focus to achieve the goals on both the reduction of urban runoff volume and the enhancement of stormwater quality. A stormwater detention system must be equipped with an infiltration bed and a permanent pool as shown in Fig ure 1.1 and Figure 1 .2 The drain time for a detention basin must be long enough to release all events at the pre development flow rates (USWDCM 2001 a )

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4 Figure 1 1 Detention System with Infiltration Pool Figure 1 2 Detention System with Perforated Plate for All Event Release Control

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5 Over the last 20 years on the learning curve of stormwater BMP, the concept of Low Impact Development (LID) was developed to treat urban runoff volumes generated from frequent rainfall events. Many research studies have been conducted to evaluate LID designs in the laboratory and in the field about their performances for various purposes Some experiments were cond ucted about the ability of heavy metal removal such as copper, lead, and zinc by using synthetic urban storm water runoff and the removal rate s based on concentration were found greater than 90% in lab experiments (Davis et al. 2001; Davis et al. 2003) and in the field experiments ( Davis et al. 2003 ). The nearly same pollutant removal abilities have been proven as rain gardens were examined by real rainfall events in the field for a period of time comparing with the results of using synthetic runoff from the lab and the field (Davis 2007; Hunt et al. 2006). Hsieh and Davis ( 2005) conducted 18 bioretention columns and 6 existing bioretention facilities using synthetic runoff under fixed hydraulic head for pollutant removals. The excellent removal of oil/gr ease was reported more than 96% while other substance removals varied significantly. For instance, the lead removal changed from 66 to more than 96%, the total suspended solids (TSS) removed from 29 to more than 96%, the phosphorus ranged from 4 to 99% and the least removal was nitrate and ammonium, the removal rates ranged from 1 to 43% and from 2 to 49%, respectively. Besides, the rain garden also has an ab ility to reduce runoff volume, peak flow, and delay time to peak (Davis 2008; Hunt et al. 2008; Li et al. 2009).

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6 Essentially, a LID design consist s of an on surface storage basin and a sub surface filtering medium that can temporarily store runoff volume and then gradually release the stored water volume through infiltrating process. A typical example i s a rain garden as shown in Figure 1.3 R ain garden was first ly introduced to the State of Maryland in 1993, and gradually has spread out as one of the most popular infiltrating practices in the USA for storm runoff treatment (PGDER 1993 ; USEPA 1999). Of course, in addition to rain garden there are many porous pavements developed for stormwater management (USWDCM 2001 a ) R ain garden is designed to have a storage basin that has a water depth of 12 inches as shown in Fig ure 1 3 The basin bottom is covered with plants and bushes. During an intense event, the basin will be filled up to 12 inch es of water the maximum water depth Y in the storage basin then the ex cess storm water overflows into the downstream manhole. The subsurface medium consists of an upper sand mix layer, with a depth Hs, a lower gravel layer, with a depth, Hg, and a sub drain system that is formed with perforated pipes networked together to drain infiltrating water into the adjacent manhole (USWDCM 2001 a ; Guo et al. 2009 a ) as sho wn in Figure 1.4.

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7 Figure 1 3 A Rain Garden Built in Denver Figure 1 4 Layout of Rain Garden

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8 The drain time of rain garden is a critical design parameter. A short drain time will not delay the peak runoff flow while a long drain time will raise the risk to have the next storm event before the basin dries up. As a common practice in stormwater infiltration, a rain garden should be designed to have a storage depth of 12 inches Assuming that the average infiltration rate is approximately 1.0 inch/hr the drain time is defaulted to be 12 hours This assumption was not verified with any field data (USWDCM 2001) The uncert ainty in rain garden operation involves the overflow risk through the storage basin and the seepage flow through the filtering layers. For instance, a newly constructed rain garden may have a high infiltration rate at 5 .0 10 .0 inch per hour (Ames et al. 2001 Guo et al. 2009 a ) although the design capacity is defaulted to be 1.0 inch/hr (USWDCM 2001 a) Over the years in use, the infiltration rate in the rain garden will be gradually reduce d due to clogging effect through the filtering layers or its drain time is increase d Li and Davis (2008a) reported that the penetration of solid s was from 2.0 to 4.0 in ches into the media when con ducted the column test and was about 7.87 inches in the field test. Some models were successfully developed to describe the above clogging phenomenon (Li and Davis 2008b; Mays and Hunt 2005). To improve a rain garden cap orifice is installed at the outlet of the perforated underdrain pipe (Guo 2012) It functions like a valve that can be adjusted to reduce the flow release according to the observation In practice, this operation relies on continuous measurements in field and often the adjustment is

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9 introduced to the rain garden as an after event effort Therefore, i t is an urgent need to have a hydrologic model that can predict the infiltration process through the storage basin and filtering medium underneath a rain garden Aided with the s a preventive measure and decision can be ma de to the rain garden to warrant a proper flow release 1.4 Objective s The objective of this study is to develop a procedure to design the storm water infiltrating system for urban runoff volume and peak flow reductions. The storage basin on surface should be sized to capture 75 to 85% of surface runoff flows while the subsurface filtering layers should be operated with the targeted flow release and drain time. To achieve this goal, the following tasks will be completed: (1) D evelop a statistical model that can represent the local population of runoff flows at the project site (2) C onduct an optimization analysis to de termine the runoff capture volume at the capture rate between 75 to 85% (3) D esign the storage basin in an infilt rating system for the opti mal runoff capture volume (4) D evelop a subsurface hydrologic model to simulate the seepage flows through the filtering layers underneath the rain garden. (5) Identify and c alibrate the model parameters

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10 (6) P redict the infiltrating process in the sand mix layer flow rel ease from rain garden through the surface to subsurface system with and without cap orifice and drain time for rain garden. (7) It is believed that this study will pr oduce a useful tool to design rain garden s and then to predict the operation of the rain garden under monitoring The design protocol derived in this study will significantly improve the current engineering practice in storm

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11 2. W ater Quality Capture Volume for Storage Basin 2.1 Introduction With the latest concept developed for better management of storm water quality and quantity controls, most urban storm water drainage systems are designed or renewed to have three layers of cascading flows. They are micro, mi nor and maj or flow systems as shown in Figure 2. 1. Figure 2 1 Micro minor major Cascading Flow Systems on Street Storm runoff generated from impervious areas shall be firstly drained onto a micro flow system for water filtering and infiltration. A micro flow system consists of porous pavers, grass swales, bio retention basins that are designed to treat the water quality capture volume up to 3 to 6 month events (Guo and Urbonas 1996). Overflows from a micro facility wil l be drained onto the minor system that consists of street inlets and storm drains. After the underground storm sewers become full, the excessive storm water will be carried on the street which is considered the major flow system. A micro drainage system is also

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12 termed low impact development (LID) facility. In practice, a LID facility is composed of surface storage basins and subsurface filtering layers. Most porous pavers are a conveyance based facility with a thin flowing water depth on the surface, whil e bio basins are a storage based facility with a storage capacity of 12 to 18 inch depth of water in the surface basin. A storage based LID is also called bio retention, rain garden, or landscaping detention basin. Rain garden is designed to improve storm water quality and to reduce runoff volumes and flows that are to be released to the downstream. A rain garden is composed with an on ground water storage basin and multiple layers of underground water filtering media. The on ground basin is sized to captu re the water quality capture volume (WQCV). WQCV was derived to maximize the capture percentage of runoff volume generated from the tributary area. WQCV varies with respect to the land use and local rainfall pattern. In the design of rain garden system, on e of the most crucial factors is to determine the storage basin volume. In the analysis of rainfall depth distribution for Denver area, it was found that 94% of a complete rainfall data series was smaller than 0.9 inch or equivalent to 1 hr, 2 yr storm eve nt (Guo and Urbonas 1996). The storm runoff inducing from these frequent, small events contains high amount of pollutants and storage basin should be sized effectively to capture most of these frequent, small events. In this stu dy, WQCV is found to be equivalent to the pre development depression loss. The performance of a LID unit under the post development condition is to mimic the natural depression loss under the pre development condition.

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13 2. 2 Review of P revious S tudies sizing design. In Mary Land, t he first 0.9 inch in an event is recommended to size the storage basin for a rain garden in the western rainfall zone and the first 1.0 inch for the eastern rain fall zone (ESD 2007). The first 1.0 inch in an event also be considered as th e basin storage for rain garden in North Carolina (Hunt and White 2001), Connecticut (Donaghue and Holcomb 2004) and New Hampsphire ( CE and NHDES 2008). In New York, 90% rainfall event number is chosen for WQCV (CWP 2010). Based on the long term hourly continuous rainfall data recorded at Stapleton Airport, Denver, Colorado, the WQCV was developed for the metro Denver area a runoff volume that is equivalent to 0.5 inch per watersh ed or the 80th percentile storm event (Urbonas et al. 1 989). Guo and Urbonas (1996) presented a set of WQCV empirical equations derived for several major metropolitan areas in the USA continent. Subsequently, the single parameter exponential distribution w as applied to produce the synthetic WQCV curve based on the mean value of local rainfall event depths (Guo and Urbonas 2002). Furthermore, a two parameter exponential model was derived based on the average rainfall event depth and incipient runoff depth to predict WQCV for storm water detention designs in South Korea (Park et al. 2011). Although all these one or two parameter statistical models were derived for WQCV calculations, none of them was sufficiently compared with field data or none of the model parameters was ever calibrated by the best fitted.

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14 In this study, the continuous one h ou r rainfall data recorded at several metro areas in the USA have been analyzed using Exponential, Log normal, Weil bull, and Gamma distributions. It was confirmed that t he 2 parameter lognormal distribution provides the best fitted for rainfall event depth population. A set of new WQCV equations was then derived using the lognormal distribution for various land uses. 2. 3 Surface Runoff Model D evelopment 2. 3 .1 Model Codes A program is written in R language (R Core T eam 201 2 ) to analyze the hourly rainfall data and to choose the best representative model for rainfall data as presented in Appendix B B ased on the best fitted model, the suitable water quality capture volume is determined for the rain garden storage basin The long term continuous hourly rainfall data were used in this study taken from several cities around the nation The program comprises three main parts: (1) the procedure for a naly zing hourly rainfall data, (2) the procedure for choosing the best fitted statistical model and (3) the procedure for d etermining the design curve for water quality capture volume of 2. 3 2 Analysis of Co mplete Rainfall Data Base 2. 3 .2.1 Rainfall D ata WQCV is derived from the long term runoff volume capture rate that is a numerical simulation of the runoff volume intercepted by surface depressed areas. Since WQCV is closely related to the local climate and rainfall pattern, it is de cided to analyze a set of rainfall data selected for several representative

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15 metropolitan areas in the US, including Boston, MA; Chicago, IL; Denver, CO; San Francisco, CA; Houston, TX; Phoenix, AZ and Seattle, WA. Their station locations are shown in Fig ur e 2 .2. All rainfall data were obtained from the National Climatic Data Center (NCDC 2013). The average length of these rainfall records is approximately 40 years and the details are summarized in Table 2. 1. In this study, the 47 year continuous hourly rain fall data recorded at the Stapleton station, City of Denver, Colorado is used as an example to illustrate how to derive the best fitted statistical model for rainfall event depth distribution Figure 2 2 Locations of Rain Gauges (Source: Google.com)

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16 Table 2 1 Summary of Rainfall Data Records Location gauge Start End Length (year) Boston, MA 01/01/1960 10/28/2008 49 Chicago, IL 01/01/1960 12/31/2007 48 Denver, CO 01/01/1965 11/01/2012 47 Houston, TX 01/01/1950 10/24/1986 37 Phoenix, AZ 11/01/1953 12/01/1983 31 San Francisco, CA 01/07/1960 04/29/2003 43 Seattle, WA 01/01/1965 12/30/2007 43 The original hourly rainfall data of the Stapleton station, Denver Colorado contain the name of the station, the date of rain and the rainfall depth for as shown in T able 2. 2 This rainfall data will be rearrange d as input file of surface numerical model for further analysis as shown in T able 2. 3 ( In the Table 2.3, the time is 24 hour clock. For example, 100 means the time is at 1.00 am, 2300 means the time is at 23.00 pm)

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17 Table 2 2 Original Hourly Rainfall Data of Denver City S tation S tation _N ame D ate Depth (100 th of an inch) COOP:052220 DENVER STAPLETON CO US 19650101 01:00 1 COOP:052220 DENVER STAPLETON CO US 19650101 11:00 1 COOP:052220 DENVER STAPLETON CO US 19650101 12:00 3 COOP:052220 DENVER STAPLETON CO US 19650101 17:00 1 COOP:052220 DENVER STAPLETON CO US 19650101 18:00 3 COOP:052220 DENVER STAPLETON CO US 19650101 19:00 2 COOP:052220 DENVER STAPLETON CO US 19650125 08:00 1 COOP:052220 DENVER STAPLETON CO US 19650128 12:00 1 COOP:052220 DENVER STAPLETON CO US 19650129 21:00 1 COOP:052220 DENVER STAPLETON CO US 19650129 22:00 2 COOP:052220 DENVER STAPLETON CO US 19650129 23:00 7 COOP:052220 DENVER STAPLETON CO US 19650130 00:00 6 COOP:052220 DENVER STAPLETON CO US 19650130 01:00 2 COOP:052220 DENVER STAPLETON CO US 19650130 02:00 5 COOP:052220 DENVER STAPLETON CO US 19650130 03:00 6 COOP:052220 DENVER STAPLETON CO US 19650130 04:00 2 COOP:052220 DENVER STAPLETON CO US 19650130 05:00 4 COOP:052220 DENVER STAPLETON CO US 19650130 06:00 4 COOP:052220 DENVER STAPLETON CO US 19650130 07:00 2 COOP:052220 DENVER STAPLETON CO US 19650130 08:00 1 COOP:052220 DENVER STAPLETON CO US 19650131 15:00 3 COOP:052220 DENVER STAPLETON CO US 19650131 16:00 3 COOP:052220 DENVER STAPLETON CO US 19650131 17:00 17 COOP:052220 DENVER STAPLETON CO US 19650131 18:00 4 COOP:052220 DENVER STAPLETON CO US 19650131 19:00 5 COOP:052220 DENVER STAPLETON CO US 19650131 20:00 3 COOP:052220 DENVER STAPLETON CO US 19650131 21:00 4 COOP:052220 DENVER STAPLETON CO US 19650131 22:00 5 COOP:052220 DENVER STAPLETON CO US 19650131 23:00 2 COOP:052220 DENVER STAPLETON CO US 19650201 01:00 1 COOP:052220 DENVER STAPLETON CO US 19650207 04:00 1 COOP:052220 DENVER STAPLETON CO US 19650207 05:00 3 ..

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18 Table 2 3 Input File for Surface Numerical Model Time Year Month Day Depth (100th of an inch ) 100 1965 1 1 1 1100 1965 1 1 1 1200 1965 1 1 3 1700 1965 1 1 1 1800 1965 1 1 3 1900 1965 1 1 2 800 1965 1 25 1 1200 1965 1 28 1 2100 1965 1 29 1 2200 1965 1 29 2 2300 1965 1 29 7 2400 1965 1 29 6 100 1965 1 30 2 200 1965 1 30 5 300 1965 1 30 6 400 1965 1 30 2 500 1965 1 30 4 600 1965 1 30 4 700 1965 1 30 2 800 1965 1 30 1 1500 1965 1 31 3 1600 1965 1 31 3 1700 1965 1 31 17 1800 1965 1 31 4 1900 1965 1 31 5 2000 1965 1 31 3 2100 1965 1 31 4 2200 1965 1 31 5 2300 1965 1 31 2 100 1965 2 1 1 400 1965 2 7 1 500 1965 2 7 3 .. .. ..

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19 2.3 .2.2 Event Separating by Inter E vent T ime A rainfall depth record is continuous in time as shown in Table 2.3. A continuous hourly rainfall depth record has to be divided into individual events based on a pre selected minimum inter event time (MIT). MIT is the period of time of no rainfall between two adjacent storm events as shown in Figure 2.3 (Driscoll et al. 1989). A rainfall event is ended when the following dry time 12 and 24 hr, are analyzed for each station. The data set with a MIT of 6 hr is used to produce the average event depth, Dm, while the other two data sets with MIT of 12 and 24 hr are used to analyze the relationship between storage volume and runoff capture rate (EPA 1983). For storm water detention designs, the MIT shall be close to the required resident time for the target sediment trap ratio for storm water quality For instance, since a rain garden is designed to have a drain time of 12 hours, the most suitable rainfall data set is the one that was created using a MIT of 12 hours because all events under the test are expected to come into an empty basin or all test rainfall events flowing through the basin are independent from the previous event. Therefore, in this study, a MIT used for rainfall event analysis is set to be the required drain time for the LID design. As expected each data set is dominated by a lar ge amount of small events with an event depth < 0.1 inch. Considering the interception losses due to vegetation and buildings, all small events < 0.1 inch were purged out of the data

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20 set (Driscoll et al. 1989; Guo and Urbonas 1996). In other words, only th e runoff producing rainfall events are considered in runoff volume capture analyses. On an average, each data set consists of 460 to 3000 individual events. The mean and standard deviation was calculated and summarized in Table 2 .4 for MIT of 6 hours. Figure 2 3 Rainfall Event Separation using MIT=12 Hours

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21 Table 2 4 Statistics for Rainfall Events using MIT=6 hours Location Number of Events Ave. Depth (in.) Standard Deviation (in.) Boston, MA 3021 0.73 0.82 Chicago, IL 2560 0.60 0.61 Denver, CO 1264 0.44 0.48 Houston, TX 1817 0.79 0.87 Phoenix, AZ 466 0.42 0.36 San Francisco, CA 1349 0.60 0.59 Seattle, WA 2987 0.50 0.56 2. 3 3 Statistical Model for Rainfall Event Depths With a selected MIT, the rainfall event depths from the 47 years of record form a sample to represent the population at the station. Figure 2.4 is an example of Box Plot (Mongtgomery and Runger 2007) and the distribution of rainfall event depths recorded at the City of De nver, Colorado using a MIT of 12 hr The histogram for the sample provides the density curve and cumulative distribution of rainfall event depths. As revealed in Fig ure 2 5 this rainfall event depth distribution is characterized with a long tailed and positive skewness. There are several probabilistic curves that portray this type of distribution, including Lognormal, Weibull, Gamma, and Exponential distributions (Mongtgome ry and Runger 2007; Bedient and Huber 2002) as shown in figure 2. 6 information criterion (AIC) is used as (Sakamoto et al., 1986):

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22 AIC = 2k 2 Ln (L) ( 2 1 ) w here k is the number of parameters in the statistical model s, and L is the maximized value of the likelihood function for th e estimated model. This criterion is based on the maximum likelihood estimates of the model parameters. Using the test data, several statistical models were evaluated with the AIC. The one with the least AIC shall be selected as the best fitted. As shown in Table 2.5 to Table 2.7 the lognormal distribution is the best fitted model for all data sets of rainfall event depth with different MIT The non exceeding probabilities from stations are also plotted with observed rainfall data as shown in Figures 2. 7 to Figure 2.1 3

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23 Figure 2 4 Boxplot and Rainfall Event Depth Distribution

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24 Figure 2 5

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25 Figure 2 6 Various Models for Distribution of Rainfall Event Depths at Denver with MIT=12 hr

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26 Table 2 5 AIC Value for Distribution of Rainfall Event Depth using MIT=6 hr Location AIC Lognormal Gamma Weibull Exponential Boston, MA 3719 4278 4377 4416 Chicago, IL 1691 2183 2343 2479 Denver, CO 55 264 373 454 Houston, TX 2381 2686 2748 2775 Phoenix, AZ 79 06 53 122 San Francisco, CA 942 1162 1236 1308 Seattle, WA 765 1531 1724 1819 Table 2 6 AIC Value for Distribution of Rainfall Event Depth using MIT=12 hr Location AIC Lognormal Gamma Weibull Exponential Boston, MA 3965 4454 4542 4579 Chicago, IL 2121 2520 2646 2763 Denver, CO 125 434 528 595 Houston, TX 2524 2785 2835 2586 Phoenix, AZ 11 90 129 183 San Francisco, CA 1251 1426 1475 1512 Seattle, WA 1863 2445 2543 2571

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27 Table 2 7 AIC Value for Distribution of Rainfall Event Depth using MIT=24 hr Location AIC Lognormal Gamma Weibull Exponential Boston, MA 4189 4602 4683 4718 Chicago, IL 2498 2831 2924 3005 Denver, CO 395 672 746 792 Houston, TX 2636 2873 2910 2920 Phoenix, AZ 73 151 186 229 San Francisco, CA 1445 1596 1622 1631 Seattle, WA 2632 3035 3059 3058 Figure 2 7 Rainfall Event Depths for Houston, TX, using MIT=6 Hours

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28 Figure 2 8 Rainfall Event Depths for San Francisco, CA, using MIT=6 Hours Figure 2 9 Rainfall Event Depths for Denver, CO, using MIT=12 Hours

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29 Figure 2 10 Rainfall Event Depths for Boston, MA, using MIT=12 Hours Figure 2 11 Rainfall Event Depths for Phoenix, AZ, using MIT=24 Hours

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30 Figure 2 12 Rainfall Event Depths for Chicago, IL, using MIT=24 Hours Figure 2 13 Rainfall Event Depths for Seattle, WA, using MIT=24 Hours

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31 2.3.4 Lognormal Distribution for WQCV The probability density function of lognormal distribution is described as: f(p) ( 2.2 ) w here p = rainfall event depth in [L], f(p) = frequency distribution, = mean of values. The cumulative probability distribution is the integration of Equation ( 2.2 ) as: ) = (2 .3 ) w o ) = the non exceedance probability, and P o = design rainfall depth in [L] selected to size the Although Equation (2 .3 ) is identified to be the best fitted for the event rainfall depth population the goal in this WQCV study is to understand the distribution of runoff volume because most LID designs are aimed at how much runoff volume is to be intercepted and treated for water quality enhancement. Therefore, the next effort is to convert the rainfall depth distribution into the runoff volume distribution. In this study, the rational method is employed because most LID designs are an on site facility serving a small urbanized ca tchment. The runoff volume can be related to rainfall depth as: d=C p ( 2.4 ) D= C P o ( 2.5 )

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32 w [L] per watershed, C = runoff coefficient. Rearranging Equation ( 2.5 ) yields: ( 2.6 ) Dividing both sides of Equation ( 2.6 ) by the mean value of rainfall depth yields: ( 2.7 ) i n which D m = mean of rainfall event depth in [L] Substituting Equation ( 2.7 ) into Equation (2 .3 ) yields: = F = ( 2.8 ) i n which C v = runoff volume capture rate (RVCR), and F = non exceeding probability for the selected design rainfall depth. RVCR represents the percentage of annual runoff volume that is intercepted and treated through the proposed rain garden with a storage volume of D (Guo and Urbonas 2002) for a the watershed imperviousness. Details can be found elsewhere (Guo and Urbonas 2013). In practic e, the engineer shall analyze the local rainfall depths to know the mean and standard deviation. Next, select a target RVCR such as 0.8 and a drain time, such as 12 hours, based on the requirement on solids removal in the local storm water enhancement crit eria.

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33 The City of Denver, CO and the City of Boston, MA are used as an example. The log mean and standard deviation are determined to be ( 1.09) inch and 0.76 inch of rainfall data recorded at the City of Boston are derived to be ( 0.57 ) inch and 0.91 inch with a MIT of 24 hours. Applying Equation capture curves are plotted as shown in Figure 2.14 and Figure 2.15 for different land uses in terms of runoff coefficients ranging from 0.3, 0.5, 0.7, 0.9 to 1.0. These curves represent the local runoff volume capture rates (RVCR) for various combinations of land use and drain time. As the size of LID storage basin increases, its RVCR increases. For a specified basin size, the RCVR decreases imperviousness increases. Figure 2 14 Runoff Volume Capture Curve for MIT=12 hr at Denver, CO

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34 Figure 2 15 Runoff Volume Capture Curve for MIT=24 hr at Boston, MA 2. 4 Geometry of Water Quality Basin With a selected runoff volume capture rate, the required storage volume, D, is determined by Figure 2.14 for Denver, CO, Figure 2.15 for Boston, MA, etc. The storage volume for the basin is calculated as: V o = D A ( 2 9 ) where V o = WQCV in [L 3 ] for storage basin, D = WQCV in [L] or [L] per watershed, A = catchment tributary area in [L 2 ]. As a common practice, the water storage depth in the basin is set to be 12 inches (USWDCM 2 001 a ). As a result, A R ( 2 10 ) w here A R = 2 ], and Y = water storage depth in [L].

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35 2. 5 Optimization A nalysis for R unoff V olume C apture R ate 2. 5 .1 Introduction A plot of RVCR is an increasing curve representing the non exceeding probability between zero and unity. In practice, both the low and high limits of a RVCR curve are asymptotic. In this study, the low and high limits for a RVCR curve are set to be from 1% to 99%. Between the two limits, the RVCR will not be dominated by the extremely small or/and large events. As illustrated in Fig ure 2.16 the trend of RVCR near the low limit for small storage basins is always on an increasing return, while the RVCR for large LID storage basi ns near the upper limit is certainly on a diminishing return. As a result, the optimal storage volume is the one that has its tangent equal to the average slope between the two limits on a RVCR curve (Guo and Urbonas 2002). Figure 2 16 Runoff Capture Curve for WQCV with C=0.5, Drain Time=12 hr at Denver, CO

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36 Referred to Figure 2.16, the average slope between the low and high limits on a RVCR curve is de r i v ed using the Log normal distribution as: / ( 2.11 ) in which S a = average slope, D 1 = lower limit of basin size in [L], and D 2 = upper limit of basin size in [L]. The slope or the tangent at a point on a RVCR curve is the value of the density function as: ( 2.12 ) in which S o = tangent on the runoff capture curve. Equating Equation (2.11) and Equation (2.12) yields: / ( 2.13 ) Equation (2.13) represents the break event point between increasing and diminishing returns. The basin volume associated with this break event point is termed WQCV (Guo and Urbonas 2002). In this study, the continuous hourly rainfall data recorded at each selected station is separated into individual events using a MIT of 12 or 24 hours. For a selected MIT, the optimal storage volume, i.e. WQCV, is derived using Equation (2.13). The WQCV is found to be related to land use, MIT or drain time, and local statistics of logarithmic values of rainfall event depths as:

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37 ( 2. 1 4 ) in which K= ratio of WQCV to mean of runoff event depth, D m As shown in Tables 2.8 and 2.9, the values of K were derived for different drain times and runoff coefficients for the selected cities in the US. Their rainfall statistics were also tabulated in Table 2.10 In general, the value of K increases with the development in the watershed approximately from 30% to 100% of the local average runoff event depth.

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38 Table 2 8 The Values of K and RVCR for Drain Time=12 hr and Various Land Uses Location C=0.3 C=0.5 C=0.7 C=0.9 C=1.0 K Cv K Cv K Cv K Cv K Cv Boston, MA 0.36 0.82 0.6 0.82 0.84 0.83 1.08 0.83 1.21 0.83 Chicago, IL 0.30 0.82 0.49 0.82 0.68 0.82 0.88 0.82 0.98 0.82 Denver, CO 0.20 0.82 0.34 0.82 0.47 0.82 0.61 0.82 0.67 0.82 Houston, TX 0.40 0.83 0.66 0.83 0.93 0.83 1.19 0.83 1.32 0.83 San Francisco CA 0.33 0.83 0.54 0.83 0.75 0.82 0.97 0.82 1.08 0.83 Seattle, WA 0.27 0.82 0.45 0.82 0.63 0.82 0.81 0.82 0.90 0.82 Phoenix, AZ 0.20 0.82 0.33 0.82 0.46 0.82 0.59 0.82 0.66 0.82 Average 0.29 0.82 0.49 0.82 0.68 0.82 0.88 0.82 0.97 0.82 Table 2 9 The Values of K and RVCR for Drain Time=24 hr and Various Land Uses Location C=0.3 C=0.5 C=0.7 C=0.9 C=1.0 K Cv K Cv K Cv K Cv K Cv Boston, MA 0.40 0.83 0.66 0.83 0.93 0.83 1.21 0.83 1.33 0.83 Chicago, IL 0.34 0.82 0.56 0.82 0.79 0.83 1.01 0.82 1.12 0.82 Denver, CO 0.22 0.82 0.38 0.82 0.53 0.82 0.68 0.82 0.75 0.82 Houston, TX 0.45 0.83 0.75 0.83 1.06 0.83 1.35 0.83 1.51 0.83 San Francisco, CA 0.40 0.83 0.67 0.83 0.93 0.83 1.20 0.83 1.34 0.83 Seattle, WA 0.38 0.83 0.63 0.83 0.88 0.83 1.14 0.83 1.27 0.83 Phoenix, AZ 0.21 0.82 0.35 0.82 0.49 0.82 0.63 0.82 0.70 0.82 Average 0.34 0.83 0.57 0.83 0.80 0.83 1.03 0.83 1.15 0.83

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39 Table 2 10 Rainfall Statistics for Selected Locations Location D m 12 hr inter event time 24 hr inter event time (in ch ) Boston, MA 0.73 0.91 0.67 0.91 0.57 Chicago, IL 0.60 0.82 0.78 0.85 0.68 Denver, CO 0.44 0.76 1.09 0.79 1.01 Houston, TX 0.79 0.91 0.58 0.93 0.47 San Francisco, CA 0.60 0.86 0.73 0.92 0.58 Seattle, WA 0.50 0.86 0.90 0.96 0.68 Phoenix, AZ 0.42 0.71 1.07 0.73 1.02 Average 0.58 0.83 0.83 0.87 0.72 2. 5 2 Design Example A case located in the City of Denver, Colorado is employed to illustrate how to use the WQCV for designs. The tributary watershed in this case is a 2.5 hectare residential area. The characteristics of solids in stormwater require a resident time of 12 hour s. As a result, the drain time of the proposed water rainfall statistics as shown in Table 2.10 the design parameters and rainfall statistics for MIT=12 hr include: D 1 = 0.007 i nch, D 2 = 0.26 inch, D m = 0. 44 inch, = 2.8 the value of K

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40 is found to be 0.34. Aided with Equation ( 2. 14), the storage volume for the proposed water quality basin is: WQCV= K D m =0.34 x 0.44 inch = 0.15 inch per watershed WQ storage volume = 0.15 inch x 2.5 hectare = 3364 ft 3 The maximum ponding depth in storage basin is recommended to be 1 area is determined as: A R = ft 2 The required storage volume for this case is 3364 cubic feet Equation ( 2. 14) is derived as a new method based on the Log normal distribution. For comparison, three WQCV methods are tested with MIT=12 or 24 hr for various land uses in terms of runoff coefficient. It is noted that the previous studies (Guo and Urbonas 1996) applied an incipient runoff depth of 0.1 inch to purge small events out of consideration. As a result, the exponential distribution was adopted for runof f depth analyses. As summarized in Table 2.11 the Log normal based method consistently gives the lowest WQCV for all tests. This tendency is due to the fact that the Log normal distribution takes more small rainfall events into consideration than does in the exponential distribution. Should an incipient runoff depth be considered in rainfall data base management? It depends on the layout of flow path. For a low impact development drainage layout, runoff flows are drained through a cascading flow path from impervious area to pervious area. On the contrary, a conventional drainage layout has two independent flow paths, including one for impervious areas and the other for pervious area. In

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41 comparison, the previous studies may be more suitable for a conventiona l drainage layout that requires a higher WQCV, while the Log normal based WQCV is for a LID layout that needs a smaller WQCV. Table 2 11 hr and 24 hr at Denver, CO C Drain Time =12 hr Drain Time =24 hr Empirical formula Log normal Empirical formula Log normal Guo & Urbonas 96 UDFCD Guo & Urbonas 96 UDFCD (inch) (inch) (inch) (inch) (inch) (inch) 0.3 0.16 0.16 0.09 0.20 0.17 0.11 0.5 0.28 0.22 0.15 0.34 0.25 0.17 0.7 0.40 0.31 0.21 0.49 0.35 0.23 0.9 0.52 0.40 0.27 0.63 0.45 0.30 2. 5 3 Conclusion In this study, the complete rainfall data base is taken into the rainfall and runoff analyses. For instance, dealing with the 100 events observed in a period of two years, the highest event has a non exceeding probability of 1%. In fact, such a magnitude is almost equivalent to the 2 yr event with a non exceeding probability of 50% when an annual maximum data base is considered. To differ from the conventional definition of non exceeding probability for extreme events, the new term of runoff capture rate is introduced in this study to represent the non exceeding probability when a complete data base is considered. Based on the diminishing return on the runoff capture rate curve, the Log normal based WQCV is determined for designing storm water quality enhancement facilities. In comparison with previous studies, the Log normal based WQCV better represents a LID layout that produces less runoff flows along a cascading flow

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42 path. Tab le 2.11 various conditions. As noticed, the WQCV is varied as a replacement of natural surface depression storage volume ranging from 0. 3 inch for watersheds with low development to 0. 1 inch for h ighly urbanized areas. When a LID facility is designed for the local Log normal based WQCV, it is expected that this basin will intercept approximately 82% of annual runoff volume for a 12 hr drain time or 83% of annual runoff volume for a 24 hr drain tim e. It is an attempt to normalize WQCV, Equation ( 2. 14), with the local cities do not lead to a generalized, single valued equation. It is concluded that the local climate is mo re a dominating factor than the development stages in a watershed. For instance, Cities of Denver and Phoenix exhibit a similarity from semi arid to arid climate, while Cities of Boston, Houston, San Francisco, Seattle are influenced by the coastal climate Further studies are needed to classify the normalized WQCV with a climate factor.

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43 3. H ydrologic M odel for I nfiltrating P rocess 3.1 Introduction As illustrated in Fig ure 3.1 a rain garden is structured as a two layered basin. The surface basin has a storage depth up to 12 inches covered with grass and plants. capture volume. The subsurface filtering layers underneath a rain garden consist of an upper s and mix layer of 18 inches and a lower gravel layer of 8 inches A sub drain system that is formed with 4 inch perf orated pipes networked together in the gravel layer to drain the infiltrating water in to the adjacent manhole (USWDCM 2001 a ; Guo et al., 2009). During an intense event, the surface basin will be filled up to its maximum capacity, and then the excess storm water overflows into the downstream manhole. The stored storm water will infiltrate slowly in to the sand mix layer and the infiltrating water will be collected by gravel layer before it flows into the manhole. The hydrologic performance of rain garden system mainly depends on infiltrating water process through the subsurface media. In this study, i t is imperative to develop a numerical subsurface model to predict the movement of wetting front through the filtering layer and drain time for the rain garden.

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44 Figure 3 1 Layout of Rain Garden (Source: UDFCD) 3. 2 Reviews of Previous S tudies There are a few models developed to simulate seepage flow through the filtering medium Dussaillant et al. (2003) developed a simple numerical model (RECARGA), which used Green Ampt equation to simulate infiltrating water under rain garden. A more complex model (RECHARGE), which applied Richards equation was also developed to model the infiltration water process below sub media (Dussaillant et al. 200 4 ). These models only focus on water recharge to groundwater system and they almost have the similar results. Heasom et al. (2006) used Green Ampt equation and Kinematic wave in HEC HMS to model rain garden system and He & Davis (2011) initiated a two equatio n.

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45 3 3 Governing Equation for Infiltrating Water Flow The hydrologic performance of a rain garden system includes the loading process into the storage basin, and the infiltrating process through the subsurface filtering media. The surface loading process is to intercept the inflow hydrograph till the storage basin becomes full. if V i
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46 in which v = seepage flow velocity in [L/T], i = hydraulic gradient for seepage flow, K s = hydraulic conductivity in [L/T], Z = vertical downward distance between torage basin, d = water depth in [L] in storage basin, = negative suction head in [L]. According to the change of moisture content in the sand layer, the infiltration rate through the bottom of the storage basin is described as: n ( 3. 4) z= downward movement of infiltrating water. As illustrated in Fig. 3. 2 the seepage flow in Equation ( 3. 2) through the sand layer must be equal to the infiltrating flow in Equation ( 3. 4) through the basin bottom. Figure 3 2 Illustration of Flows through Filtering Layer in a rain garden System The governing equation for the movement of water wetting front is derived as:

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47 ( 3.5 ) Rearranging the Eq uation ( 3.5 ), we have d z ( 3.6 ) Taking i ntegration for Equation ( 3.6 ) ( 3.7 ) T he result of this integration is: (3.8) Equation (3.8) agrees with the previous study of unsaturated seepage flows (Warrick et al. 2005). At the beginning, t=0, the rain garden is set to be empty, or d=0, and Z=0. The soil suction head in Equation (3.3) is determined by the initial soil moisture content using the sand tension moisture characteristic curve (Scheffer 2002) as shown in Figure 3.3

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48 Figure 3 3 Soil Tension Moisture Characteristic Curve (Scheffer 2002) For each time step as shown in Figure 3.4 Equation (3.8) is solved storage basin is updated by balancing the flow volumes among the inflow from the tributary watershed, the seepage flow underneath the storage basin, and the overtopping flow into the manhole. With the new depth in the storage basin, Equation (3.8) predicts the vertical movement of the wetting front. This numerical process is continued until the entire sa nd layer becomes saturated. The sand layer begins with its initial moisture content, and then is gradually filled up with water as the wetting front moves through its thickness.

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49 Figure 3 4 Sketch of Rain Garden After the wetting front reaches the bottom of the sand layer, the rain garden begins to discharge the seepage flow into the under drain pipe. The seepage (3.9) Without a cap orifice, the flow released from the rain garden must be equal to the inflow in Equation (3.9), according to the continuity of flow. As a result, the change in the water depth in the storage basin is calculated as: ( 3.10 ) in which q o 3 /T], q o (t) = seepage flow at time t released from rain garden in [L 3 /T], d(t) = water depth in [L] in storage basin at time t, H s = thickness of sand layer in [L], Q in

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50 garden in [L 3 /T], and Q o ver garden through a weir in [L3/T]. With a cap orifice, the outflow from the cap orifice is determined by orifice hydraulics as: (3.11) (3.12) in which q a ) = outflow released from cap 3 /T], C d = discharge coefficient, H t orifice, the flow released from the rain garden is the smaller between the inflow in Equation (3.9) an d the outflow in Equation (3.11) as: (3.13) For each time step, Equation (3.10) is used to determine the residual water depth in the storage basin, and Equation ( 3.13 ) is used to calculate the flow release. This computational routine is repeated until the storage basin becomes empty. During the storm event, the storage basin remains full and the excess flow overtops the basin. The seepage flow starts to decay as soon as the surface runoff dries up. As the head water depth decreases, the seepage flow rate decreases till the sand layer reaches its field capacity. As described above, both the surface and sub surface flows through the rain garden system are associated with uncertain systematic parameters, including sand conductivity and initial soil moisture content.

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51 3. 4 Procedure for S olving the G overning E quation Numerically, the water loading into the storage basin depends on the surface runoff generated from the water shed under a given rainfall event. When the runoff volume in the basin is less than the infiltration amount, the basin remains dry after each time step. Otherwise, the excessive water volume will be accumulated until the basin becomes full. After the basin is full, the maximum water depth of 12 inches will be applied to the infiltration until the basin becomes empty. The flow char t in Fig ure 3. 5 illustrates the numerical procedure for each time step. With this numerical model available, the system parameters can be calibrated with the observed seepage flows through the rain garden.

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52 Initial condition: t = 0, Q in (t)=0, Q over (t)=0, q(t)=0, d(t) =0, F(t)=0, Z(t)=0, =0.15 D full s 0.51 ft A R =400 sq.ft, Set V f (t)=0, Vx(t)=0, V(t)=0, t=5 min t = t+ t d(t+ t)= d(t) d(t)> D full Overflow Q o ver (t+ t) = Q o ver (t) Guess the infiltrating volume: Vf Let V f (t+ t) = V f (t) V(t+ t) = V(t) + Q in (t+ t). t Q over (t+ t). t V f (t+ t) d(t+ t) = V(t+ t)/A R Subsurface flow system h(t) = d(t+ t) Zn(t) = Z(t+ t) Z(t) = + h(t).Ln Let Z(t)= Zn(t) Z(t) = Zn(t) Yes No No Yes Q o ver (t+ t) = Q o ver (t)

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53 Figure 3 5 Flowchart for Numerical Subsurface Model F(t) = Z(t). F(t) < d(t+ t) Z f (t+ t) = Z f (t) + Z(t) F(t) = d(t+ t) Z(t)= F(t)/ Z f (t+ t) = Z f (t) + Z(t) F(t+ t) = F(t) + F(t) F(t+ t).A R V f (t+ t)=Vx(t+ t) Z f (t+ t)<18" q(t+ t) = 0 Yes No Yes Yes No No Fit most measured data Yes No Drain time

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54 3.5 Conclusion A subsurface numerical flow model was developed to predict the infiltration process and drain time underneath a rain garden with or without a cap orifice. This model can be easily calibrated for an existing condition. With the calibrated system parameters such as initial water content and soil hydraulic conductivity, the model can be employed to predict the future operations with a pre selected setting on the cap orifice. When the infiltration rate is higher than designed, the cap orifice shall be turned do wn to reduce the flow release. As the infiltration rate decays, the cap orifice shall be gradually turned up to maintain the proper flow release. In doing so, the rain garden will function properly with a rectified cap orifice.

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55 4. C ase Study 4 .1 Study Area The study area is located inside the residential area at the City of Lakewood, Colorado as shown in Fig ure 4.1. It consists of houses, sidewalk, driveway, asphalt road, rooftop s and lawn s The tributar y area is 83,300 sq uare feet (1.9 acre) as shown in Figure 4.2 ; of which 47 % is the impervious area The runoff coefficient for the study area is 0.30 and the average rainfall event depth for Denver metropolitan area is 0.44 inch. There are no curbs and gutters along the roadsides. A rain garde n was built in 2011 at the Nort h west corner of 21st A venue and Iris S treet. The i nlet of rain garden is located in a landscaped area between the road and a detached walk on the n orth side of 21st Avenue. This rain garden is designed to collect and analyze storm water runoff generated from a residential area. Th e rain garden system consists of 12 inch storage basin, 18 inch sand mix layer and 8 inch gravel layer. A perforated under drain pipe system is laid in the gravel layer to collect the inf iltrating water and gradually drain it to adjacent manhole. The bottom and sides of rain garden are protected with impermeable liners Therefore, all infiltrating water will be collected at the During an intense event, the storage basin will be fill ed up to its capacity and t he excess water storm will overflow in to adjacent manhole through small weir at the end of the rain garden. As soon as storm water enters the rain

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56 garden, the infiltration process begins by filling the pores in the sand mix layer. After wetting front reaches 18 inches, the gravel layer temporarily stores the filtered storm water and drains it to sewer in the downstream. Some photos of rain garden be fore and after vegetation and during operation are shown in the Figure 4. 3 4. 4 and 4. 5 respectively. Figure 4 1 Location of Rain Garden at Lakewood, CO (Source: Google.com)

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57 Figure 4 2 Tributary Watershed to Rain Garden (Source: UDFCD) Figure 4 3 Rain Garden before Growth (Source: UDFCD)

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58 Figure 4 4 The Rain Garden after Planting Vegetation (Source: UDFCD) Figure 4 5 The Rain Garden during Operation

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59 4.2 Field Data Collection 4.2.1 Rainfall Data UDFCD has recorded the rainfall data for this site since 2011. A rain gau and is protected by fence as shown in Figure 4.6 Rainfall depth is measured to 0.05 inch by a 674 tipping rain gauge. On average 14 rainfall events were recorded every year. In this study, four rainfall events have rainfall depths and durations (UDFCD 201 4 ) as shown in Table 4.1 ar e applied to evaluate the performance of the rain garden Table 4 1 Rainfall Events Applied for Rain G arden in the Study Area No Date Rainfall depth(inch) Duration (h:m) 1 May 18 201 1 1. 43 13:50 2 July 09, 2012 0.48 00:35 3 Sep 22, 2013 0.50 10:10 4 July 08, 2014 0.69 04:10

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60 Figure 4 6 A Rain Gauge at the Study Area 4.2.2 In flow M easurement Figure 4.7 to determine the storm runoff coming into the rain garden using a V Notch weir and ISCO 730 pressure transducer. The V notch cross section is two inches in he ight with an angle of 530 as shown in Figure 4.8. The ISCO 730 pressure transducer was employed to measure water depths upstream of the V notch weir and then converted water depths into flow rates.

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61 Figure 4 7 Inflow Station Figure 4 8 V notch Weir Dimension for Inflow Measurement

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62 4.2.3 Out flow M easurement The outflow station is installed in a vault at the downstream as shown in Figure 4.9 to determine the seepage flows out of the rain garden T he underdrain system was equipped with an orifice that was set to have an orifice opening diameter of 1.0 inch. The seepage flow is measured with a triangular sharp weir using the depth flow ratio curve using a 5 inch V notch weir with an angle of 20 0 as shown in Figure 4. 10 An ISCO 6712 automated sampler is used to convert flow depths into flow rates using an ISCO 730 pressure transducer housed in an underground monitoring well. Figure 4 9 Outflow Station

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63 Figure 4 10 V notch Weir Dimension for Outflow Measurement 4. 3 Calibrating the Model Parameters 4. 3 1 SWMM Model for Surface Runoff Hydrograph EPA SWMM5 was employed to predict storm water runoff hydrographs using the kinematic wave (KW) method. The study area was divided into 3 subareas as presented in Figure 4.3 These 3 subareas were converted into their equivalent rectangular planes using the KW shape factor method. Deta ils can be found elsewhere (Guo and Urbonas 2009 b ). The detailed hydrologic parameters, including watershed imperviousness, waterway slope, soil infiltration rates and depression loss, are summarized in Table 4. 2 (USWDCM 2001 b).

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64 Figure 4 11 SWMM for the Tributary Watershed Table 4 2 Land Use Characteristics of the Study Area Catchment Hydro. Parameter Depression loss Soil Infiltration ID Area Waterway Length Waterway Slope Imp. Percent Imp Area Per Area Initial rate Final rate Decay Coef. acre ft ft/ft % I n I n in /hr in/hr 1/hr 1 0.45 120.0 0.0056 65.0 0.05 0.10 3.00 0.50 4.00 2 0.68 114.0 0.0050 32.0 0.05 0.10 3.00 0.50 4.00 3 0.78 102.0 0.0072 50.0 0.05 0.10 3.00 0.50 4.00 In this study, four above rainfall events were recorded and then tested for model calibration. These observed rainfall time distributions were imported into the watershed numerical model, EPA SWMM5, for runoff simulations (Rossman 2010), and the inflow hydrograph Q versus time t were calculated for flow simulation. The resultant storm runoff flow is conveyed through the street gutters towards the rain garden. The rain garden is modeled as a shallow detention basin i n EPA SWMM5 wit h an overtopping weir to release the excess stormwater after the rain garden becomes full.

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65 Fig ure 4.12 presents the comparison of the computed and observed runoff hydrographs coming into the rain garden for May 28, 2011 event. The predicted runoff hydrog raph agrees with the observed quite well through the duration of 13 hours and 50 minutes Fig ure 13, 14 and 15 present the runoff hydrographs at the rain garden for July 9 201 2 September 22, 2013, and July 08, 201 4 events. The intercepted volume by the ra in garden is the difference between the inflow hydrograph and overtopping weir flow. It is noticed that the rain garden is so small that it only intercepted the early runoff volume and the rest of the inflow hydrograph became the overtopping flow. This fac t implies that the seepage flow underneath the rain garden is not sensitive to the inflow hydrograph as long as the basin remains full during the event. During the 4 observed events, the storage basin was filled up quickly and then remains full through the events. Figure 4 12 Computed and Observed Runoff Hydrograph for May 18, 2011 Event

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66 Figure 4 13 Runoff Volume Intercepted at Rain Garden for May 18, 2011 Event Figure 4 14 Runoff Volume Intercepted at Rain Garden for July 09, 2012 Event

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67 Figure 4 15 Runoff Volume Intercepted at Rain Garden for September 22, 2013 Event Figure 4 16 Runoff Volume Intercepted at Rain Garden for July 08, 2014 Event

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68 4.3.2 Seepage Flows from R ain Garden The initial moisture content and saturated hydraulic conductivity of sand mix layer are subsurface numerical these 4 observed cases, the soil layer underneath the rain garden was measured i =0.15 to 0.25. A range of initial moisture content and hydraulic conductiv ity was tested based on dry period between two events. The movements of wetting front through the sand layer were calculated using Equation (3.8) as soon as it rained. When the wetting front reached the gravel layer, the seepage flows were calculated by Eq uation (3.13). As illustrated in Figure 4.17 for the May 18, 2011 event the seepage flows were modeled using the high and low hydraulic conductivity coefficients. The high conductivity of 2.50 inch/hr represents the newly constructed sand layer using fresh sand mix, while the low conductivity of 1.0 inch/hr is used to simulate the clogged sand layer. The model parameters w ere calibrated based on the best fitted technique between the predicted and observed seepage flows. The fitness between the predicte d and observed was checked by the least squared error method as following equ ation: (4.1) In which MSE =mean square error, = predicted seepage flows, and Y i = observed seepage flows. F or this case, the combination of hydraulic conductivity Ks= 1.56 in/hr and initial moisture i =0.15 give the best agreement between the measured and modeled outflow s. Two other rainfall events occurred July 07 and July 19,

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69 2011 also were tested to calibrate the parameters of the mo del for this year and some figures of these cases are presented in Appendix A The average hydraulic conductivity of the sand mix layer for this year 2011 was 1.58 in/hr. The initial infiltration rate for the sand mix used in this rain garden was reported to be 3.45 10 .0 in/hr measured by a small laboratory sample (Guo et al. 2009). The reduction in its hydraulic conductivity may be caused by the possible clogging in the sand layer or the size effect b etween the sample and prototype The hydraulic conductivity should be higher because this is the first year of the rain garden in service. Figure 4 17 Observed and Predicted Seepage Flows through Sand Layer in Rain Garden for May 18, 2011 Event

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70 For the rainfall events occurred on 2012, 2013, and 2014 the predicted seepage flows also were calculated for the clean sand and clogging effects of this rai n garden a s shown in Figure 4.18 to Figure 4.20 and some more F igure s case s are presented in the Appendix A. In these cases, the observed seepage flows fit well with predicted outflows in case of clean sa nd with hydraulic conductivity Ks =2.50 in/hr for the year 2012, Ks=2.55 in/hr for the year 2013, and Ks=2.59 in/hr for the year 2014 The fluctuations in the observed flows were due to the wavy water surfaces in front of the triangular weir. Figure 4 18 Observed and Predicted Seepage Flows through Sand Layer in Rain Garden for July 09, 2012 Event

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71 Figure 4 19 Observed and Predicted Seepage Flows through Sand Layer in Rain Garden for September 22, 2013 Event Figure 4 20 Observed and Predicted Seepage Flows through Sand Layer in Rain Garden for July 08, 2014 Event

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72 4.3.3 Conclusion During 4 year study about this rain garden, the hydraulic conductivity starts with low rate of 1.56 in/hr for the first year and reaches stable rate between 2.50 in/hr and 2.59 in/hr in yea r s after. The average hydraulic conductivity Ks is determined to be 2.54 in/hr for these years The main reason for this was the roots of plants developing and worm s l iving in the mulch layer created a good connection between the mulch and sand mix layer in the second year The MSE value s for th ese rainfall events are 8.47 x 10 7 4.75 x 10 6 3. 57 x 10 6 and 3. 81 x 10 6 these MSE values imply that the data calculated from the model fit well with the measured data. 4. 4 Determining Drain Time for Rain G arden A drain time for rain garden is defined by the period of time required to drain the storage basin from its basin full dept h, 12 inches for this case, down to 1.0 inch. In this study, it was found that the asymptotic nature in the recession of seepage flow in Equation (3.9) tends to numerically prolong the drain time when the water depth becomes too shallow. Therefore, the emp ty basin in this study is defined at the residual water depth of 1.0 inch or less. A dry time is the period time, immediately after the drain time, to drain the saturated sand mix layer, 18 inches for this case, to its initial water content. The interest in this study is to detect the difference between the actual and target drain time, and how to adjust the cap orifice to meet the target drain time. Three above rainfall events occurred on July 9, 2012, September 22, 2013, and July 08, 2014 as shown in Tab le 4.1 were used to determine the drain

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73 time for this rain garden. The hydraulic conductivity of sand mix layer is stable for these year s with the average value of 2.54 in/hr. The existing orifice in the outflow station has a diameter of 1.0 inch to drain the storm runoff in the rain Based on the best agreement between the predicted and calculated by checking the water depth in the basin for each rainfall event as shown in Figure 4.21 to Figure 4.26. For these cases, drain times are 3 hours 15 minutes, 3 hours 15 minutes and 3 hours 10 minutes respectively The average drain time for this rain garden is 3 hours 13 minutes. It meant that the drain time was too fa st in comparison with the defaulted drain time of 12 hours. This rain garden works efficiently, but it does not follow the target condition that was des igned. Therefore, the rain garden nee ds a cap orifice to reduce the flow for a better water quality enha ncement. The decision making includes how much the cap orifice shall be turned down, and how to predict the future drain time after the adjustment.

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74 Figure 4 21 Observed and Predicted Seepage Flows through Rain Garden for July 9, 2012 Event Figure 4 22 Orifice Size for July 9, 2012 Event

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75 Figure 4 23 Observed and Predicted Seepage Flows through Rain Garden for September 22, 2013 Event Figure 4 24 Orifice Size for September 22, 2013 Event

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76 Figure 4 25 Observed and Predicted Seepage Flows through Rain Garden for July 08, 2014 Event Figure 4 26 Orifice Size for July 08, 2014 Event

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77 4 5 Cap O rifice Sizing Design 4. 5 .1 Procedure for Determining the D iameter of Cap O rifice In this study, a one dimension approach is applied to size the cap diameter installed at the exit of the perforated underdrain pipe to meet the required design drain time (Guo 2012). As illustrated in Figure 3.4, the steady flow is established between infiltration rate and seepage flow as: ( 4.2 ) where Q o = design flow release from rain garden in [L 3 /T]; f = infiltration rate in R = bottom area of rain garden in [L 2 ]; K s = hydraulic conductivity coefficient in [L/T] for sand mix layer; I s = hydraulic gradient through sand layer; K g = hydraulic conductivity coefficient in [L/T] for gravel lay er; and I g = hydraulic gradient through gravel layer. The drain time is calculated as: ( 4. 3 ) where T d = drain time in [T] for rain garden; and Y = water depth in [L] in full storage basin. The total headwater depth is the sum of the flow depth in t he basin, and the thicknesses of sand mix and gravel layers as: ( 4. 4 ) where H t = total hydraulic head in [L], H s = thickness of sand mix layer in [L], and H g = thickness of gravel layer in (L). The energy losses for the seepage flow th rough the sand and gravel layers are computed as: ( 4. 5 )

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78 ( 4. 6 ) s g = energy loss in gravel layer in [L]. The friction loss through the underdrain pipe is calculated as: ( 4. 7 ) N = friction loss in [L] through underdrain pipe; L = pipe length in [L]; D = for unit of feet second (10.28 for unit of meter second). As a result, the residual head applied to the cap orifice flow is: ( 4. 8 ) orifice flow. The proper cross section area for the cap orifice flow is calculated as ( 4.9 ) where A o = design opening area of cap orifice in [L 2 ]; C d = discharge coefficient; and g = gravitational acceleration in [L/T 2 ]. Equation ( 4. 9 ) provides quantifiable guidance as to how to adjust the opening area to achieve the target flow release in case a cap orifice is installed.

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79 4. 5 .2 Design E xample A prototype rain garden was built in the City of Lakewood, Colorado in 2014 (UDFCD 2014) This rain garden has been under a monitoring program for its inflows, outflows, and water quality. The rain garden consists of a storage basin and two layered filtering system. The storage basin has a flat infiltrating bed of 400 ft 2 and a storage water depth of 12 inches The sub drain pipe is 205 ft long. The thickness of the sand mix layer Hs is 18 inches and the gravel layer Hg i s 8 inches Hydraulic conductivity coefficient of sand mix is Ks = 2.5 in./h and Kg = 25 in./h for grav el layer (Guo et al. 2009). The bottom and sides of rain garden are protected with impermeable liners. As shown in the Fig ure 4.10 the underdrain system was equipped with a n orifice outlet that was set to have an orifice opening diameter of 1.0 inches Th e seepage flow is measured with a triangular sharp weir using the depth flow ratio curve. The range of infiltration rate for growing media of rain garden is about 10.0 1.0 in./h during its life cycle. To meet the required drain time of 12 hours, the cap o rifice is designed to reduce flow release to 1.0 in./h r The procedure for calculating the area of cap orifice is determined as follow: Q f A R x 400 0.009 3 cfs The energy gradient and loss th rough the sand layer are I s 0.4 h s I s H s 0.4 18 7.2

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80 The energy gradient and loss through the gravel layer are I g 0.04 h g I g H g 0.04 The friction loss through underdrain pipe is h N h N 4.62 x 2 20 x 0.053 With C d = 0.70, the cross sectional area of cap orifice is determined as A o = 0.001 ft 2 T he cross sectional area of orifice is 0.001 ft 2 or the diameter is 0.44 inc h. Orifice Installation T he cap orifice will be installed at the exit of the perforated underdrain pipe as shown in Figure operation, three above rainfall events also are used to predict the outflow and drain time for the rain garden. The underdrain system now is equipped with a cap orifice that can be adjusted the orifice opening diameter from 0.44 in to 1.0 in. In this study, th ree different sizes of the cap orif ice are used for consideration : ( 1) the existing diameter d= 1.0 inch ( 2) the opening diameter d= 0.7 inch and (3) the opening diameter d= 0.44 inch.

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81 Figure 4 27 Adjustment using Valve for Seepage Flows As discussed in section 4.3, three rainfall events were used to calibrate the model parameters, including the hydraulic conductivity in the sand mix layer and the initial soil water content These model parameters were determined based on the best fitted technique b etween the observed and predicted seepage flows for the existing condition After that, the seepage flow model with the known calibrated parameters w as used to predict the future r with different adjustment on the cap orifice using Equation 3.9 ), ( 3.11 ), and ( 3.13 ). For this case, an investigation was conducted on two operational settings on the orifice, including open diameters of 0.7 inch and 0.44 inch. The predicted seepage flows from numerical simulations for both orifice settings are also plotted in Figure 4.21, Figure 4.23 and Figure 4.25. The predicted drain times storage for the rain garden become 4.75 hr after th e cap orifice is turned down to the open diameter of 0.7 inch and 12 hr for the open diameter of 0.44 inch as

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82 shown in Figure 4.21 to Figure 4.26 Although it will take months and years to collect adequate data for verification, this case study presents a calibration process of an existing rain garden and demonstrate the predictions for its future performance after an adjustment on its cap orifice It is noticed that the seepage flow is controlled by the infiltrating rate through the soil mix layer when the orifice is widely open such as the open diameter of 1.0 inch On the contrary, when the operational setting is turned down to allow a slow flow, such as the open diameter of 0.7 inch the orifice flow becomes dominating. As expected, when the open diameter is 0.7 inch the early flow is controlled by the orifice, while the final flow is dominated by the infiltrating rate. The demarcation for this flow switch is the break point shown in Figure 4.21, Figure 4.23 and Figure 4.25.

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83 5. C onclusions 5.1 Green Concept Impacts of urbanization on stormwater are summarized into two major categories: (1) increase of runoff volume, and (2) increase of peak flo ws. Since effective means to reduce peak flows. A water detention process only temporarily stores the excessive stormwater for a slow release, but it does not reduce the water volume. Since 1990, the low impact development concept was developed to promote on site storm water infiltration in order to reduce the increased runoff volume. A LID device, including rain garden, must be installed at the upstream low point where is a runoff so urce. At the regional outfall point, a stormwater detention may be needed if the design peak flows exceed the downstream conveyance capacity in the existing waterway. The green concept in stormwater management is essentially a strategy on how to lay out a set of LID devices for upstream runoff volume reduction and a regional downstream detention system to reduce peak flow releases. All LID devices shall be designed to cope with the small and frequent event, while the detention basin shall be designed to saf ely pass the extreme events (2 yr to 100 yr event). As demonstrated in this study, the small and frequent event for LID design is approximately the 80 th percentile value on the on site runoff depth distribution curve. After an extensive reviews and tests, the log normal distribution was identified to be the best representative curve for urban runoff depth distributions.

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84 To further demonstrate how to integrate the rain garden built in this study into a future detention system to achieve an all over stormwate r green management, the drainage system in the test watershed is modeled for its future fully developed condition with an imperviousness percentage of 80 %. 5.2 Evaluation of Green Stormwater Management The proposed detention basin is located at the south west corner of the intersection of Iris Street and 21 st Avenue as shown in Figure 5.1. The watershed link node system used in the SWMM model is also marked on Figure 5.1. Figure 5.1 SWMM Model Layout of Test Watershed

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85 There are f our scenarios investigated in this study: (1) Pre development condition as the baseline hydrologic condition, (2) Post development condition without any flow release control, (3) Post development condition with a 100 yr flood detention basin, and ( 4 ) Post development condition with a 10 and 100 yr flood detention basin to reduce the extreme flows and a rain garden to reduce frequent flows. 5.2.1 Detention Basin Sizing Stage Storage Relationship Using the impervious percentage of 10% as the basis the 100 yr peak flow must be reduced from the post development flow release of 9.59 cfs to 2.81 cfs, while the 10 yr peak flow must be reduced from the post development flow release of 4.98 cfs to 0.40 cfs. In this case, setting the peak outflow to be th e peak outflow under the pre development condition, the after detention hydrograph is approximated by a linear rising hydrograph (Guo 1999, and 2006) as shown in Figure 5.2. The required storm water detention volumes were found to be 0.22 ac ft for the 100 yr event and 0.18 acre ft for the 10 yr event. Considering a triangular basin as shown in Figure 5.3, the bottom area of the detention basin is a 35 ft by 60 ft triangle. According to the side slope described in Table 5.1, the stage storage curve is deve loped using triangular cross sections. The 10 yr and 100 yr water depths in this basin under design are identified to be 4 and 4.5 feet.

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86 Figure 5.2 Detention Volume Determined by Hydrograph Methods Figure 5.3 Sketch of Flood Detention for 10 to 10 0 yr Events

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87 Table 5.1 Stage Area Storage for Proposed Detention Basin Water Surface Elevation Basin Side Slope Width of Cross Section Length of Cross Section Cross Sectional Pond Area Accumulated Storage Identify Design Water Elevation feet ft/ft feet feet acres sq ft acre ft cf 5602.00 4.00 35.00 60.00 0.02 1050.0 0.00 0.0 5602.50 4.00 39.00 64.00 0.03 1248.0 0.01 574.5 5603.00 4.00 43.00 68.00 0.03 1462.0 0.03 1252.0 5603.50 4.00 47.00 72.00 0.04 1692.0 0.05 2040.5 5604.00 4.00 51.00 76.00 0.04 1938.0 0.07 2948.0 5604.50 4.00 55.00 80.00 0.05 2200.0 0.09 3982.5 5605.00 4.00 59.00 84.00 0.06 2478.0 0.12 5152.0 5605.50 4.00 63.00 88.00 0.06 2772.0 0.15 6464.5 5606.00 4.00 67.00 92.00 0.07 3082.0 0.18 7928.0 10 yr 5606.50 4.00 71.00 96.00 0.08 3408.0 0.22 9550.5 100 yr 5607.00 4.00 75.00 100.00 0.09 3750.0 0.26 11340.0 5607.50 4.00 79.00 104.00 0.09 4108.0 0.31 13304.5 Freeboard 5.2.2 Outlet Vault for Flow Release Control Stage Outflow Curve The outlet vault is formed using orifices as the flow collection element, and outfall culverts serve as the discharge element. For this case, two alternatives are developed to collect stormwater into the outlet vault from the detention basin, including (A) the orifices sized to control the 100 yr release only, or (B) the orifices designed to have a full spectrum control on all flow releases. For Case (A) in Figure 5.4, a horizontal grate of 0.7 by 07 ft square horizontal grate is placed at a vertical dista nce of 4.25 ft above the basin floor and a vertical side orifice of 6.6 inch in diameter is placed on the floor. For Case (B) in Figure 5.5, in addition to the top horizontal grate described in Case (A), a box orifice of 2.5x5.0 inch is installed to contr ol the 10 yr flow

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88 release, and a perforated plate with two one inch holes is placed to control small events. Figure 5.4 Outlet for 100 yr Release Control for Case (A) Figure 5.5 Outlet for Full Spectrum Release Control for Case (B)

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89 As shown in Figur e 5.6, the outfall culvert is designed using a pipe of 12 inches in diameter with a length of 200 feet laid on a slope at 1.0 percent. Knowing that the tailwater surface elevation is at 5600.50 feet as shown in Figure 5.6, the outflow released from the out let vault is the smaller between the flow collected from the orifices and flow discharged through the culvert pipe. Table 5.2 summarizes the stage outflow relationship for the detention basin under design. Figure 5.6: Outfall Pipe and Culvert Hydraulics

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90 Table 5.2 Stage Outflow for Detention Basin System Stage Collection capacity Culvert Release Total Outflow Orifice Plate Box Orifice Horizontal Grate Total ft cfs cfs cfs cfs cfs cfs 5602.00 0.00 0.00 0.00 0.00 0.00 0.00 5602.50 0.01 0.00 0.00 0.01 4.22 0.01 5603.00 0.02 0.00 0.00 0.02 4.48 0.02 5603.50 0.05 0.00 0.00 0.05 4.72 0.05 5604.00 0.06 0.00 0.00 0.06 4.95 0.06 5604.50 0.07 0.00 0.00 0.07 5.17 0.07 5605.00 0.08 0.00 0.00 0.08 5.38 0.08 5605.50 0.09 0.03 0.00 0.12 5.58 0.12 5606.00 0.10 0.18 0.00 0.27 5.78 0.27 5606.50 0.10 0.25 0.77 1.12 5.97 1.12 5607.00 0.11 0.31 1.33 1.74 6.15 1.74 5607.50 0.12 0.35 1.71 2.18 6.33 2.18 A rating curve is the relationship between flow capacity and water depth in a detention basin. Applying the orifice and weir formulas to the top grate in Case (A), the rating curve is developed in Figure 5.7. The maximum flow release under the condition of basin full is slightly less than the 100 yr pre development peak flow.

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91 Figure 5.7: Stage Ou tflow for 100 yr Flood Control Repeat the same procedure in Case (A). The rating curve for Case (B) is derived as shown in Figure 5.8. The major difference between Figures 5.7 and 5.8 is that the top grate and side orifice used in Case (A) can effectively reduce the 100 yr event, but they have no control on small events because all small flows are in a situation of flowing through. Case (B) shows that the top grate and box orifice can well control the flow releases for extreme events, while the perforated plate regulates the small flows at release rates under the pre development condition.

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92 Figure 5.8: Stage O utflow for Full Spectrum Release Control 5.2.3 T est on Storm water G reen M anagement For all scenarios, the Colorado 2 hr design rainfall curves are used to simulate the 2 5 10 50 and 100 year events. The performance of the detention system is further evaluated by the 30 year hourly continuous rainfall data recorded at the Stapleton Airport Station, Denver, Colorado from 1948 through 1978. The f ormer will exam the detention effectiveness on the extreme events, while the later will evaluate the control on the frequent events. The results of the flow releases from the study watershed are summarized in Figure 5.9 for the extreme events and Figure 5. 10 for 30 yr hourly rainfall data. The red line represents the flow frequency curve under the post development condition. The blue line represents the flow frequency curve under the pre development condition. The difference between the post and pre develo pment requires a storm water mitigation plan. The black line represents the alternative with a 100 yr detention basin, i.e. Case (A). It shows that the 100 yr peak flow is

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93 reduced via the detention process to its pre development condition, but it does not have an effective control on the rest of the flows. On the contrary, the simulation for Case (B) using a perforated plate, it can mimic the 2 to 100 yr outflows under the pre development condition. The slow release through the perforated plate prolongs th e resident time for the stored water volume. The slow flow release will not trigger bed and bank erosion in the downstream channel. For frequent events, the storage basin associated with the rain garden provides a storage volume of on e ft depth in a basin of 400 sq u a re feet. As demonstrated in Figure 5.11, all small and frequent events are well controlled to mimic the flow releases under the pre development condition. This test numerically verifies that the stormwater green management can be achieved using LID units as a runoff source control for small events (<3 to 6 month event) and an outlet detention basin for peak flow reduction for extreme events. Figure 0 .9 Outflows Release from Test Watershed for All Events

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94 Figure 0 .10 Outflows Release from Test Watershed for 30 year Rainfall Data at Denver City Figure 0 .11 Outflows Release from Test Watershed for More Frequent Events

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95 5.3 Summary and Conclusion (1) Analyses of 40 yr long term continuous rainfall records for 7 metropolitan areas in the US indicate that the best fitted model for describing the runoff event depth population is the log normal distribution. The optimization technique applied to log normal distribution produces a set of empirical equations for estimating WQCV for stormwater LID designs. The suitable size of WQCV for storm water quality control facilities is an ab ility of runoff volume from the complete rainfall series, especially from small, more frequent rainfall events. In this study, the long term rainfall data records from seven cities in US were analyzed to find the best models to describe the rainfall event depths from selected stations. The results of this analysis reveal that the lognormal distribution is the best fitted model for determining the proper basin size of WQCV. The analysis indicates that the findings can apply to any cities in the US based on their local average rainfall depths. The optimization procedure was also examined for these cities based on the concept of diminishing return. It was found that the optimal runoff volume capture rate is about 82% for 12 hr drain time, and 83% for 24 hr dra in time. The basin size determined by this study is smaller than previous studies because the 2 parameter model better describe the rainfall data, it considers the mean and the standard deviation of rainfall event depths in calculation while other studies only

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96 consider one parameter (Guo and Urbonas 2002) or none parameter ( USWDCM 2010) verified. (2) A surface to subsurface hydrologic model was developed to predict the water infiltration process through the unsaturated to saturated sand mix layers. The flow re lease and drain time of the rain garden can be calibrated and then serves for future flow predictions. In this study, the storage basin of the rain garden under design is sized to capture the water quality capture volume (WQCV) that is determined using the log normal distribution to describe the population of rainfall event depths. The subsurface filtering layers are sized to achieve the targeted flow release and drain time. A surface subsurface hydrologic model is developed in this study to simulate the wa ter loading process in the storage basin, and also the infiltrating process through the sand mix layer. Based on field tests and data, this hydrologic model is further calibrated to determine the best fitted values for soil initial moisture content and hyd raulic conductivity involved in the flow simulations. The calibration process may be conducted using the high low game to find the best fitted value using the least square method. This calibrated model is a useful tool to understand the clogging situation in the rain garden, and also helps the engineer make operational decisions on drain time and flow releases from the rain garden. (3) A cap orifice was introduced to adjust the drain time for a rain garden to meet with the required flow release.

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97 The performance of a rain garden is very sensitive to its drain time. The drain time is determined by the infiltration rate through the filtering layers and the operation of the cap orifice at the exit of the underdrain system. Often, the laboratory tests do not warrant the same performance for the as built because of the modeling scale effect. Therefore the cap orifice is a practical tool for flow adjustments through the life cycle of a rain garden. The simplified, one dimensional model developed in this study, has been tested with the 4 year field data collected at the test site. It was proved to be useful in data calibration and can predict the future performance for the pre selected cap orifice settings. This study presents the detailed loading and unlo ading processes of wetting front movement through the unsaturated to saturated zones underneath a rain garden. Since the sand mix layer is homogeneous in both the horizontal and vertical directions, the one dimensional flow model works well. In case of com plicated sub drain network or exfiltration between the rain garden and surrounding native soils, the model may have to be expanded into a two dimensional flow net for collecting infiltrating water. For a small neighborhood rain garden less than 200 square meters, the numerical procedure derived in this study is very useful and helpful to assist the engineer to have a quantifiable assessment on flow adjustment using a cap orifice. The latest development on the web based automation process can control orific operations from a distance. The technology of remote sensing and automation will implement the model developed in this study much easily for rain garden designs and operations.

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98 REFERENCES Ames, B. C., Emily, L. L., Lonna, M. F., & William B. R. (2001). "Preliminary assessment of infiltration rates and effects on water quality of selected infiltration media for use in highway runoff retention basins in Wasington state". WA RD5122, Dept. of Transportation, Olympia, WA. Athayde, D. (1976). Best management practices (BMP). Urban Stormwater Seminars, WPD 03 76 04. Washington, D.C: U.S. Environmental Protection Agency. Bedient, P. B., & Huber, W. C. (2002). Hydrology and Floodplain Analysis. Third Edition, Prentice Hall, Upper Saddle Ri ver, NJ. Bogue, D. J. (1955). Urbanism in the United State s 1950. American Journal of Sociology 60(5) 471 486. Booth, D. B., & Jackson, C. (1997). Urbanization of Aquatic Systems Degradation Thresholds, Stormwater Detention, and the Limits of Mitigation. Water Resources Bulletin Vol. 33, 1077 1090. CE, & NHDES. (2008). Comprehensive Environmental Inc and New Hampshire Department of Environmental Services, New Hampshire Stormwater Manual Volume 2. CWP. (2010). Center for Watershed Protection, Stormwater Management Design Manual. Albany, NY 12233. Davis, A. P. (2007). Field Performance of Bioretention: Water Quality. Enviromental Engineering Science 24(8), 1048 1063. Davis, A. P. (2008). Field Performance of Bioretention: Hydrology Impacts. Journal of Hydrologic Engineering 13(2), 90 95. Davis, A. P., Shokouhian, M., Sharma, H., & Minami, C. (2001). Laboratory Study of Biological Retention for Urban Stormwater Management. Water Environment Research 73(1),5 14. Davis, A. P., Shokouhian, M., Sharma, H., Minami, C., & Winogradoff, D. (2003). Water Quality Improvement through Bioretention: Lead, Copper, and Zinc Removal. Water Environment Research 75(1), 73 82. DeGroen, C. (2012). State Demography Office Annual Meeting. Colorado Department of Local Affairs: Denver, Colorado. Donaghue, A., & Holcomb, M. (2004). Connecticut Stormwater Quality Manual. Connecticut Department of Environmental Protection.

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99 Driscoll, E. D., Palhegyi, G. E., Strecker, E. W., & Shelley, P. E. (1989). Analysis of Storm Ev ents Characteristics for Selected Rainfall Gauges throughout the United States. U.S. Environmental Protection Agency, Washington, D.C Dussaillant, A. R., Cozzetto, K., Brander, K., & Potter, K. W. (2003). Green Ampt Model of a rain garden and Comparison t o Richard's Equation Model. Sustainable Planning and Development, the Sustainable World, WIT, Southampon, SO, U.K. 891 900. Dussaillant, A. R., Wu, C. H., & Potter, K. W. (2004). Richards Equation Model of a Rain Garden. Journal of Hydrologic Engineering 9(3), 219 225. Environmental Services Division (ESD). (2007). Bioretention Manual. The Prince George's County, Maryland. EPA. (1983). Results of The Nationwide Urban Runoff Program. Washington, DC.: Final Report, U.S. Enviromental Protection Agency, NTIS No. PB84 185545. Guo,J.C. (1999). Detention Storage Volume for Small Urban Catchment Journal of Water Resources Planning and Management, 125(6) ,380 382 Guo, J. C. (2006). Urban hydrology and hydraulics design. Highlands Ranch, Colorado: Water Resources Pu blications, LLC. Guo, J. C. (2012). Cap Orifice as a Flow Regulator for Rain Garden Design. Journal of Irrigation and Drainage Engieering 138(2),198 202. Guo, J. C., & Urbonas, B. (1996). Maximized Detention Volume Determined by Runoff Capture Ratio. Jour nal of Water Resources Planning and Management 122(1), 33 39. Guo, J. C., & Urbonas, B. (2002). Runoff Capture and Delivery Curves for Storm water Quality Control Designs. Journal of Water Resources Planning and Management 128(3), 208 215. Guo, J. C., & Urbonas, B. (2009 b). Conversion of Natural Watershed to Kinematic Wave Cascading Plane. Journal of Hydrologic Engineering 14(8), 839 846. Guo, J. C., Shauna, K. M., & Anu, R. (2009 a). Design of two layered porous landscaping detention basin. Journal of Environmental Engineering 135(2), 1268 1274. Guo, J. Y., & Ben, U. (2013). Volume Based Runoff Coefficients for Urban Catchments. Journal of Irrigation and Drainage Engineering He, Z., & Davis, A. P. (2011). Process Modeling of Storm Water Flow in a Bior etention Cell. Journal of Irrigation and Drainage Engineering 121 131.

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100 Heasom, W., Traver, R. G., & Welker, A. (2006). Hydrologic Modeling of A Bioinfiltration Best Management practice. Journal of The American Water Resources Association 1329 1347. Hsieh, C. h., & Davis, A. P. (2005). Evaluation and Optimization of Bioretention Media for Treatment of Urban Storm Water Runoff. Journal of Enviromental Engineering 131(11), 1521 1531. Hunt, W. F., & White, N. (2001). Designing Rain Gardens (Bio Retenti on Areas). North Carolina Cooperative Extension Service. Hunt, W. F., Jarrett, A. R., Smith, J. T., & Sharkey, L. J. (2006). Evaluating Bioretention Hydrology and Nutrient removal at Three Field Sites in North Carolina. Journal of Irrigation and Drainage E ngineering 132(6), 600 608. Hunt, W. F., Smith, J. T., Jadlocki, S. J., Hathaway, J. M., & Eubanks, P. R. (2008). Pollutant Removal and Peak Flow Mitigation by a Bioretention Cell in Urban Charlotte, North Carolina. Journal of Enviromental Enginering 134 (5), 403 408. Li, H., & Davis, A. P. (2008a). "Urban particle capture in bioretention media. I: Laboratory and field studies.". Journal of Environmental Engineering 134(6), 409 418. Li, H., & Davis, A. P. (2008b). Urban Particle Capture in Bioretention M edia. II: Theory and Model Development. Journal of Environmental Engineering 134(6), 419 432. Li, H., Sharkey, L. J., Hunt, W. F., & Davis, A. P. (2009). Mitigation of Impervious Surface Hydrology Using Bioretention in North Carolina and Maryland. Journal of Hydrologic Engineering 14(4), 407 415. Mays, D. C., & Hunt, J. R. (2005). Hydrodynamic Aspects of Particle Clogging in Porous Media. Environmental Science & Technology 39(2), 577 584. Mongtgomery, D. C., & Runger, G. C. (2007). Apllied Statistics and Probability for Engineers. John Wiley & Sons, Inc. National climatic Data Center (NCDC). (2013). Climate Data Online: Datasets Retrieved 02 19, 2014, from http://www.ncdc.noaa.gov/cdo web/datasets Park, D., Song, Y. I., & Roesner, L. A. (2011). The Effec t of the Seasonal Rainfall Distribution on Storm Water Quality Capture Volume Estimation. Journal of Water Resources Planning and Management PGDER. (1993). Prince George's County Department of Environmental Resources. Design Mannual for Use of Bioretentio n in Storm water Management.

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101 R Core Team. (2012). R: A Language and Environment for Statistical, R Foundation for Statistical Computing,Vienna, Austria. ISBN 3 900051 07 0, http://www.R project.org/. Rossman, L. A. (2010). Storm Water Management Model. Ohi o: EPA/600/R 05/040. Sakamoto, Y., Ishiguro, M., & Kitagawa, G. (1986). Akaike Information Criterion Statistics. D. Reidel Publishing Company. Scheffer, F. (2002). Lehrbuch der Bodenkunde. / Scheffer / Schachtschabel. 15. Aufl. Spektrum Akademischer Verlag Heidelberg. UDFCD. (2014). Urban Drainage and Flood Control District, Rain Garden at West 21st Avenue and Iris Street. Lakewood, Colorado. UNHABITAT. (2010). Urban trends: Urban and Economic Growth Retrieved 12 29, 2013, from http://www.unhabitat.org/do cuments/sowc10/r7.pdf United State Census Bureau. (2010). 2010 Census Urban and Rural Classification and Urban Area Criteria Retrieved 11 18, 2014, from http://www.census.gov/geo/reference/ua/urban rural 2010.html United State Census Bureau. (2010). 2010 Census Urban Lists Record Layouts Retrieved 11 18, 2013, from http://www.census.gov/geo/reference/ua/ualists_layout.html United State Census Bureau. (2012). World Population:1950 2050 Retrieved 02 19, 2014, from http://www.census.gov/population/international/data/idb/worldpopgraph.php Urbonas, B., Guo, J. C., & Tucker, L. S. (1989). Sizing a Capture Volume for Stormwater Quality Enhancement. Flood Hazard News. Urban Drainage and Flood Control District, Denver, Col orado USEPA. (1999). Stormwater Technology Fact Sheet Bioretention. Office of Water, Washington D.C EPA 832 F 99 012. USWDCM. (2001 a). Urban Storm Water Drainage Criteria Mannual, volume 3, Best Management Practices. Urban Drainage and Flood Control Dis trict, Denver, Colorado. USWDCM. (2001 b). Urban Storm Water Drainage Criteria Mannual, Volume 1. Urban Drainage and Flood Control District, Denver, Colorado. Warrick, A. W., Zerihun, D., Sanchez, C. A., & Furman, A. (2005). Infiltration under Variable Pon ding Depths of Water. Journal of Irrigation and Drainage Engineering 131(4), 358 363. "Washington Area NURP Project." (1983). Rep., Prepared for metropolitan Washington Council of Government Occoquan Watershed Monitoring Laboratory, Manassas, Va.

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102 APPENDIX A. Some Other Rainfall Events Applied in the Case Study Table A 1. Rainfall Events Applied for Rain Garden in the Study Area No Date Rainfall depth(inch) Duration (h:m) 1 July 07, 2012 1. 38 08 : 1 0 2 July 07, 2011 1.73 07:05 3 July 19, 2011 0.57 02:05 Figure A 1 Runoff Volume Intercepted at Rain garden for July 07, 2012 Event

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103 Figure A 2 Observed and Predicted Seepage Flows through Sand Layer in Rain Garden for July 07, 2012 Event Figure A 3 Runoff Volume Intercepted at Rain garden for July 07, 201 1 Event

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104 Figure A 4 Observed and Predicted Seepage Flows through Sand Layer in Rain Garden for July 07, 2011 Event Figure A 5 Runoff Volume Intercepted at Rain garden for July 19 2011 Event

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105 Figure A 6 Observed and Predicted Seepage Flows through Sand Layer in Rain Garden for July 19 2011 Event

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106 B. The Surface and Sub Surface Numerical Model s B1. Codes of t he Surface Numerical Model Codes for the surface numerical model are written in R language which can download free at the website http://cran.r project.org/bin/windows/base/ R is used for statistical computation and graphics. Th e surface numerical model has three procedures as follow s : ########################################################### ####### PROCEDURE I: ANALYZING HOURLY RAINFALL DATA ##### ###### Step 1: Calculation of dried period ############### data=read.table ("Denver.txt",header=FALSE) hour=data[,1] year=data[,2] month=data[,3] day=data[,4] a=length(year) y29=scan("dt.txt") # # on the list is greater than the latest year has data in the rainfall input file (this b=length(y29) z=1:b j=c(y29) k=c(4,6,9,11) l=1:4 dp=1:a # dried period

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107 xtemp = 1:6 for (i in 1:a 1) {#0 for (z in c(y29)) {#z is y29 if (identical(all.equ al(data[i+1,2],data[i,2]), TRUE)) {#1equal year if (identical(all.equal(data[i+1,3],data[i,3]), TRUE)){#2equal month dp[i]=((data[i+1,4] data[i,4])*24+((data[i+1,1] data[i,1])/100) 1) } else {#2Not equal month if (identical(all.equal(data[i,3],2), TRUE)){#3 if (identical(all.equal(data[i,2],z), TRUE)) { dp[i]=((data[i+1,3] data[i,3] 1)*30*24+(29 data[i,4]+data[i+1,4])*24 ((data[i,1] data[i+1,1])/100) 1)} else { dp[i]=((data[i+ 1,3] data[i,3] 1)*30*24+(28 data[i,4]+data[i+1,4])*24 ((data[i,1] data[i+1,1])/100) 1)} } else {#3 Not month 2 for (l in k) { if (identical(all.equal(data[i,3],l), TRUE)){dp[i]=((data[i+1,3] data[i,3] 1)*30*24+(30 data[i,4]+da ta[i+1,4])*24 ((data[i,1] data[i+1,1])/100) 1)} else {dp[i]=((data[i+1,3] data[i,3] 1)*30*24+(31 data[i,4]+data[i+1,4])*24 ((data[i,1] data[i+1,1])/100) 1)} } }#3 }#2 } else {#1 Not equal year if (identical(all.equal(data[i+1,3],data[i,3]), TRUE)) {#2 beginning equal month if (data[i,4]<=data[i+1,4]) {dp[i]=((data[i+1,2] data[i,2])*365*24+(data[i+1,4] data[i,4])*24 ((data[i,1] data[i+1,1])/100) 1)} else {

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108 dp[i]=((data[i+1,2] data[i,2])*365*24 (data[i,4] data[i+1,4])*24 ((data[i,1] data[i+1,1])/100) 1) } } else {#2 beginning not equal month if (identical(all.equal(data[i,3],2), TRUE)) {#3 if (iden tical(all.equal(data[i,2],z),TRUE)) dp[i]=((data[i+1,2] data[i,2] 1)*365*24+(12 data[i,3]+data[i+1,3] 1)*30.5*24+(29 data[i,4]+data[i+1,4])*24 ((data[i,1] data[i+1,1])/100) 1) else dp[i]=((data[i+1,2] data[i,2] 1)*365* 24+(12 data[i,3]+data[i+1,3] 1)*30.5*24+(28 data[i,4]+data[i+1,4])*24 ((data[i,1] data[i+1,1])/100) 1) } else {#3 not month 2 for (l in k) { if (identical(all.equal(data[i,3],l), TRUE)){ dp[i]=((data[i+1,2] data[i,2] 1)*365*24+(12 d ata[i,3]+data[i+1,3] 1)*30.5*24+(30 data[i,4]+data[i+1,4])*24 ((data[i,1] data[i+1,1])/100) 1)} else { dp[i]=((data[i+1,2] data[i,2] 1)*365*24+(12 data[i,3]+data[i+1,3] 1)*30.5*24+(31 data[i,4]+data[i+1,4])*24 ((data[i,1] data[i+1,1]) /100) 1)} } }#3 Ending not equal month }#2 } #1Ending not equal year }#z } xtemp = 1:6 for (i in 1:a 1) xtemp = rbind(xtemp,c(data[i,1],data[i,2],data[i,3],data[i,4],data[i,5],dp[i]))

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109 nt = length(xtemp[,1]) write(t(xtemp[2:nt,]), file="result_of_dp1.txt", ncol=6, sep=" \ t") ### Step 2: Calculation of dried period:repairing month 2 & 4,6,9,11 ###### data=read .table("result_of_dp1.txt",header=FALSE) hour=data[,1] year=data[,2] month=data[,3] day=data[,4] a=length(year) xtemp = 1:6 for (i in 1:a 1) {#0 if (identical(all.equal(data[i+1,2],data[i,2]), TRUE)) {#1equal year if (identical( all.equal(data[i+1,3],data[i,3]), TRUE)) {next} else {#2 not equal month if (identical(all.equal(data[i,3],2), TRUE)){#3 if (data[i,2]==1968) data[i,6]=((data[i+1,3] data[i,3] 1)*30*24+(29 data[i,4]+data[i+1,4])*24 ((data[i,1] data[ i+1,1])/100) 1) if (data[i,2]==1972) data[i,6]=((data[i+1,3] data[i,3] 1)*30*24+(29 data[i,4]+data[i+1,4])*24 ((data[i,1] data[i+1,1])/100) 1) if (data[i,2]==1976) data[i,6]=((data[i+1,3] data[i,3] 1)*30*24+(29 data[i,4]+data[ i+1,4])*24 ((data[i,1] data[i+1,1])/100) 1) if (data[i,2]==1980) data[i,6]=((data[i+1,3] data[i,3] 1)*30*24+(29 data[i,4]+data[i+1,4])*24 ((data[i,1] data[i+1,1])/100) 1) if (data[i,2]==1984) data[i,6]=((data[i+1,3] da ta[i,3] 1)*30*24+(29 data[i,4]+data[i+1,4])*24 ((data[i,1] data[i+1,1])/100) 1)

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110 if (data[i,2]==1988) data[i,6]=((data[i+1,3] data[i,3] 1)*30*24+(29 data[i,4]+data[i+1,4])*24 ((data[i,1] data[i+1,1])/100) 1) if (data[i,2]==19 92) data[i,6]=((data[i+1,3] data[i,3] 1)*30*24+(29 data[i,4]+data[i+1,4])*24 ((data[i,1] data[i+1,1])/100) 1) if (data[i,2]==1996) data[i,6]=((data[i+1,3] data[i,3] 1)*30*24+(29 data[i,4]+data[i+1,4])*24 ((data[i,1] data[i+1,1])/100) 1) if (data[i,2]==2000) data[i,6]=((data[i+1,3] data[i,3] 1)*30*24+(29 data[i,4]+data[i+1,4])*24 ((data[i,1] data[i+1,1])/100) 1) if (data[i,2]==2004) data[i,6]=((data[i+1,3] data[i,3] 1)*30*24+(29 data[i,4]+data[i+1,4])*24 ((data[i,1] da ta[i+1,1])/100) 1) if (data[i,2]==2008) data[i,6]=((data[i+1,3] data[i,3] 1)*30*24+(29 data[i,4]+data[i+1,4])*24 ((data[i,1] data[i+1,1])/100) 1) if (data[i,2]==2012) data[i,6]=((data[i+1,3] data[i,3] 1)*30*24+(29 data[i,4]+data[i+1,4 ])*24 ((data[i,1] data[i+1,1])/100) 1) } else {#3 not month 2 if (identical(all.equal(data[i,3],4),TRUE)) data[i,6]=((data[i+1,3] data[i,3] 1)*30*24+(30 data[i,4]+data[i+1,4])*24 ((data[i,1] data[i+1,1])/100) 1) if (identical(all.equal(data[i,3],6),TRUE)) data[i,6]=((data[i+1,3] data[i,3] 1)*30*24+(30 data[i,4]+data[i+1,4])*24 ((data[i,1] data[i+1,1])/100) 1) if (identical(all.equal(data[i,3],9),TRUE)) data[i, 6]=((data[i+1,3] data[i,3] 1)*30*24+(30 data[i,4]+data[i+1,4])*24 ((data[i,1] data[i+1,1])/100) 1) if (identical(all.equal(data[i,3],11),TRUE)) data[i,6]=((data[i+1,3] data[i,3] 1)*30*24+(30 data[i,4]+data[i+1,4])*24 ((data[i,1] data[i+ 1,1])/100) 1) }#3 end not month 2

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111 }#2 } else {#1 #if (identical(all.equal(data[i+1,2],data[i,2]),TRUE)) {next} else {#1 not equal year if (identical(all.equal(data[i+1,3],data[i,3]),TRUE)) {#2 equal month if (identical(all.equal(data[i,3],2), TRUE)){#3 if (data[i,2]==1968) data[i,6]=((data[i+1,2] data[i,2] 1)*365*24+(12 data[i,3]+data[i+1,3] 1)*30*24+(29 data[i,4]+data[i+1,4])*24 ((data[i,1] data[i+1,1])/100) 1) if (dat a[i,2]==1972) data[i,6]=((data[i+1,2] data[i,2] 1)*365*24+(12 data[i,3]+data[i+1,3] 1)*30*24+(29 data[i,4]+data[i+1,4])*24 ((data[i,1] data[i+1,1])/100) 1) if (data[i,2]==1976) data[i,6]=((data[i+1,2] data[i,2] 1)*365*24+(12 data[i,3]+data[ i+1,3] 1)*30*24+(29 data[i,4]+data[i+1,4])*24 ((data[i,1] data[i+1,1])/100) 1) if (data[i,2]==1980) data[i,6]=((data[i+1,2] data[i,2] 1)*365*24+(12 data[i,3]+data[i+1,3] 1)*30*24+(29 data[i,4]+data[i+1,4])*24 ((data[i,1] data[i+1,1])/100) 1) i f (data[i,2]==1984) data[i,6]=((data[i+1,2] data[i,2] 1)*365*24+(12 data[i,3]+data[i+1,3] 1)*30*24+(29 data[i,4]+data[i+1,4])*24 ((data[i,1] data[i+1,1])/100) 1) if (data[i,2]==1988) data[i,6]=((data[i+1,2] data[i,2] 1)*365*24+(12 data[i,3]+data[i+1, 3] 1)*30*24+(29 data[i,4]+data[i+1,4])*24 ((data[i,1] data[i+1,1])/100) 1) if (data[i,2]==1992) data[i,6]=((data[i+1,2] data[i,2] 1)*365*24+(12 data[i,3]+data[i+1,3] 1)*30*24+(29 data[i,4]+data[i+1,4])*24 ((data[i,1] data[i+1,1])/100) 1) if (da ta[i,2]==1996) data[i,6]=((data[i+1,2] data[i,2] 1)*365*24+(12 data[i,3]+data[i+1,3] 1)*30*24+(29 data[i,4]+data[i+1,4])*24 ((data[i,1] data[i+1,1])/100) 1)

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112 if (data[i,2]==2000) data[i,6]=((data[i+1,2] data[i,2] 1)*365*24+(12 data[i,3]+data[i+1,3] 1)*30*24+(29 data[i,4]+data[i+1,4])*24 ((data[i,1] data[i+1,1])/100) 1) if (data[i,2]==2004) data[i,6]=((data[i+1,2] data[i,2] 1)*365*24+(12 data[i,3]+data[i +1,3] 1)*30*24+(29 data[i,4]+data[i+1,4])*24 ((data[i,1] data[i+1,1])/100) 1) if (data[i,2]==2008) data[i,6]=((data[i+1,2] data[i,2] 1)*365*24+(12 data[i,3]+data[i+1,3] 1)*30*24+(29 data[i,4]+data[i+1,4])*24 ((data[i,1] data[i+1,1])/100) 1) if (da ta[i,2]==2012) data[i,6]=((data[i+1,2] data[i,2] 1)*365*24+(12 data[i,3]+data[i+1,3] 1)*30*24+(29 data[i,4]+data[i+1,4])*24 ((data[i,1] data[i+1,1])/100) 1) }#3 } else {#2 not equal month if (identical(all.equal(data[i,3],2), TRUE )){#3 if (data[i,2]==1968) data[i,6]=((data[i+1,2] data[i,2] 1)*365*24+(12 data[i,3]+data[i+1,3] 1)*30*24+(29 data[i,4]+data[i+1,4])*24 ((data[i,1] data[i+1,1])/100) 1) if (data[i,2]==1972) data[i,6]=((data[i+1,2] data[i,2] 1)*365*24+(12 data[i, 3]+data[i+1,3] 1)*30*24+(29 data[i,4]+data[i+1,4])*24 ((data[i,1] data[i+1,1])/100) 1) if (data[i,2]==1976) data[i,6]=((data[i+1,2] data[i,2] 1)*365*24+(12 data[i,3]+data[i+1,3] 1)*30*24+(29 data[i,4]+data[i+1,4])*24 ((data[i,1] data[i+1,1 ])/100) 1) if (data[i,2]==1980) data[i,6]=((data[i+1,2] data[i,2] 1)*365*24+(12 data[i,3]+data[i+1,3] 1)*30*24+(29 data[i,4]+data[i+1,4])*24 ((data[i,1] data[i+1,1])/100) 1) if (data[i,2]==1984) data[i,6]=((data[i+1,2] data[i,2] 1)*365*24+( 12 data[i,3]+data[i+1,3] 1)*30*24+(29 data[i,4]+data[i+1,4])*24 ((data[i,1] data[i+1,1])/100) 1) if (data[i,2]==1988) data[i,6]=((data[i+1,2] data[i,2] 1)*365*24+(12 data[i,3]+data[i+1,3] 1)*30*24+(29 data[i,4]+data[i+1,4])*24 ((data[i,1] data[i+ 1,1])/100) 1)

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113 if (data[i,2]==1992) data[i,6]=((data[i+1,2] data[i,2] 1)*365*24+(12 data[i,3]+data[i+1,3] 1)*30*24+(29 data[i,4]+data[i+1,4])*24 ((data[i,1] data[i+1,1])/100) 1) if (data[i,2]==1996) data[i,6]=((data[i+1,2] data[i,2] 1)*365*24+(12 data[i,3]+data[i+1,3] 1)*30*24+(29 data[i,4]+data[i+1,4])*24 ((data[i,1] data[i+1,1])/100) 1) if (data[i,2]==2000) data[i,6]=((data[i+1,2] data[i,2] 1)*365*24+(12 data[i,3]+data[ i+1,3] 1)*30*24+(29 data[i,4]+data[i+1,4])*24 ((data[i,1] data[i+1,1])/100) 1) if (data[i,2]==2004) data[i,6]=((data[i+1,2] data[i,2] 1)*365*24+(12 data[i,3]+data[i+1,3] 1)*30*24+(29 data[i,4]+data[i+1,4])*24 ((data[i,1] data[i+1,1])/100) 1) if ( data[i,2]==2008) data[i,6]=((data[i+1,2] data[i,2] 1)*365*24+(12 data[i,3]+data[i+1,3] 1)*30*24+(29 data[i,4]+data[i+1,4])*24 ((data[i,1] data[i+1,1])/100) 1) if (data[i,2]==2012) data[i,6]=((data[i+1,2] data[i,2] 1)*365*24+(12 data[i,3]+data[i+1,3] 1 )*30*24+(29 data[i,4]+data[i+1,4])*24 ((data[i,1] data[i+1,1])/100) 1) } else {#3 not month 2 if (identical(all.equal(data[i,3],4), TRUE)) data[i,6]=((data[i+1,2] data[i,2] 1)*365*24+(12 data[i,3]+data[i+1,3] 1)*30.5*24+(30 data[i,4 ]+data[i+1,4])*24 ((data[i,1] data[i+1,1])/100) 1) if (identical(all.equal(data[i,3],6), TRUE)) data[i,6]=((data[i+1,2] data[i,2] 1)*365*24+(12 data[i,3]+data[i+1,3] 1)*30.5*24+(30 data[i,4]+data[i+1,4])*24 ((data[i,1] data[i+1,1])/100) 1) if (identical(all.equal(data[i,3],9), TRUE)) data[i,6]=((data[i+1,2] data[i,2] 1)*365*24+(12 data[i,3]+data[i+1,3] 1)*30.5*24+(30 data[i,4]+data[i+1,4])*24 ((data[i,1] data[i+1,1])/100) 1) if (identical(all.equal(data[i,3 ],11), TRUE)) data[i,6]=((data[i+1,2] data[i,2] 1)*365*24+(12 data[i,3]+data[i+1,3] 1)*30.5*24+(30 data[i,4]+data[i+1,4])*24 ((data[i,1] data[i+1,1])/100) 1) }#3 end not month 2 }#2

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114 }#1 } xtemp = 1:6 for (i in 1:a 1) xtemp = rbind(xtemp,c(data[i,1],data[i,2],data[i,3],data[i,4],data[i,5],data[i,6])) nt = length(xtemp[,1]) write(t(xtemp[2:nt,]), file="result_of_dp2.txt", ncol=6, sep=" \ t") ############# End calculate dried period ##################### ##### ####Step 3: Calculation of dry period of 6,12,24,48_hour rainfall event #### ######### 3 1: Calculation of dry period_6hr ################## data=read.table("result_of_dp2.txt",header=FALSE) a=length(data[,6]) xtemp =1:2 for (i in 1:a) if (da ta[i,6]>=6) ## dryperiod >= 6 hours xtemp = rbind(xtemp,c(i,data[i,6])) nt = length(xtemp[,1]) write(t(xtemp[2:nt,]), file="drp6.txt", ncol=2,sep=" \ t" ) ######## 3 2: Calculation of dry period_12hr #################### xtemp =1:2 for (j in 1:a) if (data[j,6]>=12) ## dryperiod >= 12 hours## xtemp = rbind(xtemp,c(j,data[j,6]))

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115 nt = length(xtemp[,1]) write(t(xtemp[2:nt,]), file="drp12.txt", ncol=2, sep=" \ t") ######## 3 3: Calculation of dry period_24hr ##################### xtemp = 1:2 for (z in 1:a) if (data[z,6]>=24) ## dryperiod >= 24 hours xtemp = rbind(xtemp,c(z,data[z,6])) nt = length(xtemp[,1]) write(t(xtemp[2:nt,]), file="drp24.txt", ncol=2, sep=" \ t") ######## 3 4: calculation of dry period_48hr ##################### xtemp = 1:2 for (k in 1:a) if (data[k,6]>=48) ## dryperiod >=48 hours xtemp = rbind(xtemp,c(k,data[k,6])) nt = length(xtemp[,1]) write(t(xtemp[2:nt,]), file="drp48.txt", ncol=2, sep=" \ t") ####### Step 4: calculation of 6,12,24,48 hour rainfall depth ########## # ###### 4 1: calculation of 6 hour rainfall depth ################# data=read.table("result_of_dp2.txt",header=FALSE) d=read.table("drp6.txt", header=FALSE) b=length(d[,1]) a=length(data[,5]) c=a

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116 z=1:b rf=1:b r6=1:b r=1:c j=c(d[,1]) dr6=1:b for (z in 1:b) for (i in 1:j[z]) r[i]=data[i,5] r=cumsum(r) for (z in 1:b) for (i in j[z]) rf[z]=r[i]/100 if (i< 1) r6[i]=rf[i] for (i in 1:b) { r6[i+1]=rf[i+1] rf[i] } xtemp = 1:2 for (i in 1:b) xtemp = rbind(xtemp,c(r6[i],d[i,2])) nt = length(xtemp[,1]) write(t(xtemp[2:nt,]), file="rainfall&driedperiod_6.txt", ncol=2, sep=" \ t") ####### 4 2: calculation of 12 hour rainfall depth #################

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117 data=read.table("result_of_dp2.txt",header=FALSE) d=read.table("drp12.txt", header=FAL SE) b=length(d[,1]) a=length(data[,5]) c=a z=1:b rf=1:b r12=1:b r=1:c j=c(d[,1]) dr12=1:b for (z in 1:b) for (i in 1:j[z]) r[i]=data[i,5] r=cumsum(r) for (z in 1:b) for (i in j[z]) rf[z]=r[i]/100 if (i< 1) r12[i]=rf[i] for (i in 1:b) { r12[i+1]=rf[i+1] rf[i] } xtemp = 1:2 for (i in 1:b)

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118 xtemp = rbind(xtemp,c(r12[i],d[i,2])) nt = length(xtemp[,1]) write(t(xtemp[2:nt,]), file="rainfall&driedperiod_12.txt", ncol=2, sep=" \ t") ####### 4 3: calculation of 24 hour rainfall depth ################# data=read.table("result_of_dp2.txt",header=FALSE) d=read.table("drp24.txt", header=FALSE) b=length(d[,1]) a=length(data[,3]) c=a z=1:b rf=1:b r24=1:b r=1:c j=c(d[,1]) dr24=1:b for (z in 1:b) for (i in 1:j[z]) r[i]=data[i,5] r=cumsum(r) for (z in 1:b) for (i in j[z]) rf[z]=r[i]/100 if (i< 1) r24[i]=rf[i]

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119 for (i in 1:b) { r24[i+1]=rf[i+1] rf[i] } xtemp = 1:2 for (i in 1:b) xtemp = rbind(xtemp,c(r24[i],d[i,2])) nt = length(xtemp[,1]) write(t(xtemp [2:nt,]), file="rainfall&driedperiod_24.txt", ncol=2, sep=" \ t") ####### 4 4: calculation of 48 hour rainfall depth ################# data=read.table("result_of_dp2.txt",header=FALSE) d=read.table("drp48.txt", header=FALSE) b=length(d[,1]) a=length(dat a[,5]) c=a z=1:b rf=1:b r48=1:b r=1:c j=c(d[,1]) dr48=1:b for (z in 1:b) for (i in 1:j[z]) r[i]=data[i,5]

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120 r=cumsum(r) for (z in 1:b) for (i in j[z]) rf[z]=r[i]/100 if (i< 1) r48[i]=rf[i] for (i in 1:b) { r48[i+1]=rf[i+1] rf[i] } xtemp = 1:2 for (i in 1:b) xtemp = rbind(xtemp,c(r48[i],d[i,2])) nt = length(xtemp[,1]) write(t(xtemp[2:nt,]), file="rainfall&driedperiod_48.txt", ncol=2, sep=" \ t") ##Step 5: calculation of rainfall duration for 6,12,24,48 hour rainfall event #### ## 5 1: Rainfall duration for 6 hour rainfall event ####################### data=read.table("result_of_dp2.txt",header=FALSE) d=read.table("drp6.txt", header=FALSE) j1=c(d[,1]) hour=data[,1] year=data[,2] month=data[,3] day=data[,4] a=length(j1)

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121 dr6 =1:a y29=scan("dt.txt") b=length(y29) z=1:b j=c(y29) k=c(4,6,9,11) l=1:4 dp=1:a if (i< 1) (dr6[i]=((data[j1[i],4] data[i,4])*24+((data[j1[i],1] data[i,1])/100)+1)) for (i in 1:a 1) {#0 for (z in c(y29)) {#z if (identical(all.equal (data[j1[i+1],2],data[j1[i]+1,2]), TRUE)) {#1equal year if (identical(all.equal(data[j1[i+1],3],data[j1[i]+1,3]), TRUE)){#2equal month dr6[i+1]=((data[j1[i+1],4] data[j1[i]+1,4])*24+((data[j1[i+1],1] data[j1[i]+1,1])/100)+1) } else {#2Not equal month if (identical(all.equal(data[j1[i]+1,3],2), TRUE)){#3 if (identical(all.equal(data[j1[i]+1,2],z), TRUE)) { dr6[i+1]=((data[j1[i+1],3] data[j1[i]+1,3] 1)*30*24+(29 data[j1[i]+1,4]+data[j1[i+1],4])*24+((data[j1[i+1],1] data[j1[i]+1,1])/100)+1)} else { dr6[i+1]=((data[j1[i+1],3] data[j1[i]+1,3] 1)*30*24+(28 data[j1[i]+1,4]+data[j1[i+1],4])*2 4+((data[j1[i]+1,1] data[j1[i+1],1])/100)+1)} } else {#3 Not month 2 for (l in k) {

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122 if (identical(all.equal(data[j1[i]+1,3],l), TRUE)){dr6[i+1]=((data[j1[i+1],3] data[j1[i]+1,3] 1)*30*24+(30 data[j1[i]+1,4]+data[j1[i+1],4])*24 +((data[j1[i+1],1] data[j1[i]+1,1])/100)+1)} else {dr6[i+1]=((data[j1[i+1],3] data[j1[i]+1,3] 1)*30*24+(31 data[j1[i]+1,4]+data[j1[i+1],4])*24+((data[j1[i+1],1] data[j1[i]+1,1])/100)+1)} } }#3 }#2 } } } xtemp = 1:2 for (i in 1:a) xtemp = rbind(xtemp,c(dr6[i],data[j1[i],6])) nt = length(xtemp[,1]) write(t(xtemp[2:nt,]), file="result_of_6hour_duration.txt", ncol=2, sep=" \ t") data=read.table("result_of_6hour_duration.txt",header=FALSE) d= read.table("rainfall&driedperiod_6.txt", header=FALSE) y=data[,2] dr=d[,1] a=length(y) b=length(dr) xtemp = 1:3 for (i in 1:a) xtemp = rbind(xtemp,c(d[i,1],data[i,1],data[i,2]))

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123 nt = length(xtemp[,1]) write(t(xtemp[2:nt,]), file="result_of_rainf all_duration_driedperiod_6.txt", ncol=3, sep=" \ t") ### 5 2: Rainfall duration for 12 hour rainfall event #################### data=read.table("result_of_dp2.txt",header=FALSE) d=read.table("drp12.txt", header=FALSE) j1=c(d[,1]) hour=data[,1] year= data[,2] month=data[,3] day=data[,4] a=length(j1) dr6=1:a y29=scan("dt.txt") b=length(y29) z=1:b j=c(y29) k=c(4,6,9,11) l=1:4 dp=1:a if (i< 1) (dr12[i]=((data[j1[i],4] data[i,4])*24+((data[j1[i],1] data[i,1])/100)+1)) for (i in 1:a 1) {#0 for (z in c(y29)) {#z if (identical(all.equal(data[j1[i+1],2],data[j1[i]+1,2]), TRUE)) {#1equal year

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124 if (identical(all.equal(data[j1[i+1],3],data[j1[i]+1,3]), TRUE)){#2equal month dr12[i+1]=((data[j1[i+1],4] data[j1[i]+1,4])*24+( (data[j1[i+1],1] data[j1[i]+1,1])/100)+1) } else {#2Not equal month if (identical(all.equal(data[j1[i]+1,3],2), TRUE)){#3 if (identical(all.equal(data[j1[i]+1,2],z), TRUE)) { dr12[i+1]=((data[j1[i+1],3] data[j1[i]+1,3] 1)*30*24+(29 data[j1[i]+1,4]+data[j1[i+1],4])*24+((data[j1[i+1],1] data[j1[i]+1,1])/100)+1)} else { dr12[i+1]=((data[j1[i+1],3] data[j1[i]+1,3] 1)*30*24+(28 data[j1[i]+1,4]+data[j1[i+1],4])*24+((data[j1[i]+1,1] data[j1[i+1],1])/ 100)+1)} } else {#3 Not month 2 for (l in k) { if (identical(all.equal(data[j1[i]+1,3],l), TRUE)){dr12[i+1]=((data[j1[i+1],3] data[j1[i]+1,3] 1)*30*24+(30 data[j1[i]+1,4]+data[j1[i+1],4])*24+((data[j1[i+1],1] data[j1[i]+1,1])/100)+1)} else {dr12[i+1]=((data[j1[i+1],3] data[j1[i]+1,3] 1)*30*24+(31 data[j1[i]+1,4]+data[j1[i+1] ,4])*24+((data[j1[i+1],1] data[j1[i]+1,1])/100)+1)} } }#3 }#2 } } } xtemp = 1:2 for (i in 1:a) xtemp = rbind(xtemp,c(dr12[i],data[j1[i],6])) nt = length(xtemp[,1])

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125 write(t(xtemp[2:nt,]), file="result_of_12hour _duration.txt", ncol=2, sep=" \ t") data=read.table("result_of_12hour_duration.txt",header=FALSE) d=read.table("rainfall&driedperiod_12.txt", header=FALSE) y=data[,2] dr=d[,1] a=length(y) b=length(dr) xtemp = 1:3 for (i in 1:a) xtemp = rbind(xtemp,c (d[i,1],data[i,1],data[i,2])) nt = length(xtemp[,1]) write(t(xtemp[2:nt,]), file="result_of_rainfall_duration_driedperiod_12.txt", ncol=3, sep=" \ t") ### 5 3: Rainfall duration for 24 hour rainfall event ###################### data=read.table("result_ of_dp2.txt",header=FALSE) d=read.table("drp24.txt", header=FALSE) j1=c(d[,1]) hour=data[,1] year=data[,2] month=data[,3] day=data[,4] a=length(j1) dr6=1:a

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126 y29=scan("dt.txt") b=length(y29) z=1:b j=c(y29) k=c(4,6,9,11) l=1:4 dp=1:a if (i< 1) (dr24[i]=((data[j1[i],4] data[i,4])*24+((data[j1[i],1] data[i,1])/100)+1)) for (i in 1:a 1) {#0 for (z in c(y29)) {#z if (identical(all.equal(data[j1[i+1],2],data[j1[i]+1,2]), TRUE)) {#1equal year if (identical(all.equal (data[j1[i+1],3],data[j1[i]+1,3]), TRUE)){#2equal month dr24[i+1]=((data[j1[i+1],4] data[j1[i]+1,4])*24+((data[j1[i+1],1] data[j1[i]+1,1])/100)+1) } else {#2Not equal month if (identical(all.equal(data[j1[i]+1,3],2), TRUE)) {#3 if (identical(all.equal(data[j1[i]+1,2],z), TRUE)) { dr24[i+1]=((data[j1[i+1],3] data[j1[i]+1,3] 1)*30*24+(29 data[j1[i]+1,4]+data[j1[i+1],4])*24+((data[j1[i+1],1] data[j1[i]+1,1])/100)+1)} else { dr24[i+1] =((data[j1[i+1],3] data[j1[i]+1,3] 1)*30*24+(28 data[j1[i]+1,4]+data[j1[i+1],4])*24+((data[j1[i]+1,1] data[j1[i+1],1])/100)+1)} } else {#3 Not month 2 for (l in k) {

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127 if (identical(all.equal(data[j1[i]+1,3],l), TRUE)){dr24[i+1] =((data[j1[i+1],3] data[j1[i]+1,3] 1)*30*24+(30 data[j1[i]+1,4]+data[j1[i+1],4])*24+((data[j1[i+1],1] data[j1[i]+1,1])/100)+1)} else {dr24[i+1]=((data[j1[i+1],3] data[j1[i]+1,3] 1)*30*24+(31 data[j1[i]+1,4]+data[j1[i+1],4])*24+((data[j 1[i+1],1] data[j1[i]+1,1])/100)+1)} } }#3 }#2 } } } xtemp = 1:2 for (i in 1:a) xtemp = rbind(xtemp,c(dr24[i],data[j1[i],6])) nt = length(xtemp[,1]) write(t(xtemp[2:nt,]), file="result_of_24hour_duration.txt", ncol=2, sep=" \ t") data=read.table("result_of_24hour_duration.txt",header=FALSE) d=read.table("rainfall&driedperiod_24.txt", header=FALSE) y=data[,2] dr=d[,1] a=length(y) b=length(dr) xtemp = 1:3 for (i in 1:a) xtemp = rbind(xtemp,c (d[i,1],data[i,1],data[i,2])) nt = length(xtemp[,1])

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128 write(t(xtemp[2:nt,]), file="result_of_rainfall_duration_driedperiod_24.txt", ncol=3, sep=" \ t") ### 5 4: Rainfall duration for 48 hour rainfall event ###################### data=read.table("result_ of_dp2.txt",header=FALSE) d=read.table("drp48.txt", header=FALSE) j1=c(d[,1]) hour=data[,1] year=data[,2] month=data[,3] day=data[,4] a=length(j1) dr6=1:a y29=scan("dt.txt") b=length(y29) z=1:b j=c(y29) k=c(4,6,9,11) l=1:4 dp=1:a if (i< 1) (dr48[i]=((data[j1[i],4] data[i,4])*24+((data[j1[i],1] data[i,1])/100)+1)) for (i in 1:a 1) {#0 for (z in c(y29)) {#z if (identical(all.equal(data[j1[i+1],2],data[j1[i]+1,2]), TRUE)) {#1equal year

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129 if (identical(all.equal(data[j1[i+1],3] ,data[j1[i]+1,3]), TRUE)){#2equal month dr48[i+1]=((data[j1[i+1],4] data[j1[i]+1,4])*24+((data[j1[i+1],1] data[j1[i]+1,1])/100)+1) } else {#2Not equal month if (identical(all.equal(data[j1[i]+1,3],2), TRUE)){#3 if (identical(all.equal(data[j1[i]+1,2],z), TRUE)) { dr48[i+1]=((data[j1[i+1],3] data[j1[i]+1,3] 1)*30*24+(29 data[j1[i]+1,4]+data[j1[i+1],4])*24+((data[j1[i+1],1] data[j1[i]+1,1])/100)+1)} else { dr48[i+1]=((data[j1[i+1],3 ] data[j1[i]+1,3] 1)*30*24+(28 data[j1[i]+1,4]+data[j1[i+1],4])*24+((data[j1[i]+1,1] data[j1[i+1],1])/100)+1)} } else {#3 Not month 2 for (l in k) { if (identical(all.equal(data[j1[i]+1,3],l), TRUE)){dr48[i+1]=((data[j1[i+1],3 ] data[j1[i]+1,3] 1)*30*24+(30 data[j1[i]+1,4]+data[j1[i+1],4])*24+((data[j1[i+1],1] data[j1[i]+1,1])/100)+1)} else {dr48[i+1]=((data[j1[i+1],3] data[j1[i]+1,3] 1)*30*24+(31 data[j1[i]+1,4]+data[j1[i+1],4])*24+((data[j1[i+1],1] data[j1 [i]+1,1])/100)+1)} } }#3 }#2 } } } xtemp = 1:2 for (i in 1:a) xtemp = rbind(xtemp,c(dr48[i],data[j1[i],6])) nt = length(xtemp[,1])

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130 write(t(xtemp[2:nt,]), file="result_of_48hour_duration.txt", ncol=2, sep=" \ t") data=read.table("result_of_48hour_duration.txt",header=FALSE) d=read.table("rainfall&driedperiod_48.txt", header=FALSE) y=data[,2] dr=d[,1] a=length(y) b=length(dr) xtemp = 1:3 for (i in 1:a) xtemp = rbind(xtemp,c(d[i,1],data[i,1],data[i,2])) n t = length(xtemp[,1]) write(t(xtemp[2:nt,]), file="result_of_rainfall_duration_driedperiod_48.txt", ncol=3, sep=" \ t") ######### Step 6: Calculation of storm events that produce runoff ########## ##### Runoff=[Rainfall_depth incipient runoff depth(=0.1 inch) >0] ######### ######## 6 1: Storm event with separation time period = 6 hours ########### data6=read.table("result_of_rainfall_duration_driedperiod_6.txt",header=FALSE) Rainfall_depth=data6[,1] Rainfall_duration=dat a6[,2] Dried_period=data6[,3] l=length(Rainfall_depth) xtemp = 1:3 for (i in 1:l) if (data6[i,1]>0.1)

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131 (xtemp = rbind(xtemp,c((data6[i,1]),data6[i,2],data6[i,3]))) nt = length(xtemp[,1]) write(t(xtemp[2:nt,]), file="result_of_rainfall_duration_dried period_6(produce_runoff).txt", ncol=3, sep=" \ t") #write data to file #### 6 2: Storm event with separation time period = 12 hours ############ data12=read.table("result_of_rainfall_duration_driedperiod_12.txt",header=FALS E) Rainfall_depth=data12[,1] Rainfall_duration=data12[,2] Dried_period=data12[,3] l=length(Rainfall_depth) xtemp = 1:3 for (i in 1:l) if (data12[i,1]>0.1) (xtemp = rbind(xtemp,c((data12[i,1]),data12[i,2],data12[i,3]))) nt = length(xtemp[,1]) write(t(xtemp[2:nt,]), file="result _of_rainfall_duration_driedperiod_12(produce_runoff).txt", ncol=3, sep=" \ t") #write data to file #### 6 3: Storm event with separation time period = 12 hours ############# data24=read.table("result_of_rainfall_duration_driedperiod_24.txt",header=FALS E) Rainfall_depth=data24[,1] Rainfall_duration=data24[,2] Dried_period=data24[,3]

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132 l=length(Rainfall_depth) xtemp = 1:3 for (i in 1:l) if (data24[i,1]>0.1) (xtemp = rbind(xtemp,c((data24[i,1]),data24[i,2],data24[i,3]))) nt = length(xtemp[,1]) write(t( xtemp[2:nt,]), file="result_of_rainfall_duration_driedperiod_24(produce_runoff).txt", ncol=3, sep=" \ t") #write data to file ### 6 4: Storm event with separation time period = 48 hours ############## data48=read.table("result_of_rainfall_duration_driedper iod_48.txt",header=FALS E) Rainfall_depth=data48[,1] Rainfall_duration=data48[,2] Dried_period=data48[,3] l=length(Rainfall_depth) xtemp = 1:3 for (i in 1:l) if (data48[i,1]>0.1) (xtemp = rbind(xtemp,c((data48[i,1]),data48[i,2],data48[i,3]))) nt = length(xtemp[,1]) write(t(xtemp[2:nt,]), file="result_of_rainfall_duration_driedperiod_48(produce_runoff).txt", ncol=3, sep=" \ t") #write data to file ### Step 7: Calculation average depth,standard deviation, skewness coef, interevent time for storm ev ents ##########

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133 source("skew.txt") # MIT=6 hours # data6=read.table("result_of_rainfall_duration_driedperiod_6(produce_runoff).txt", header=FALSE) n=length(data6[,1]) #number_of_events duration6=data6[,2] dur6_mean=mean(duration6) raindepth6=data6[ ,1] n=length(data6[,1]) #number_of_events raindepth6_mean=mean(raindepth6) raindepth6_vars=var(raindepth6) raindepth6_sd=sd(raindepth6) raindepth6_skew=skew(raindepth6) Inter_event_time6=data6[,3] Ave_inter_event_time6=mean(Inter_event_time6) # MIT =12 hours # data12=read.table("result_of_rainfall_duration_driedperiod_12(produce_runoff).tx t",header=FALSE) n=length(data12[,1]) #number_of_events duration12=data12[,2] dur12_mean=mean(duration12) raindepth12=data12[,1] n=length(data12[,1]) #number _of_events raindepth12_mean=mean(raindepth12)

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134 raindepth12_vars=var(raindepth12) raindepth12_sd=sd(raindepth12) raindepth12_skew=skew(raindepth12) Inter_event_time12=data12[,3] Ave_inter_event_time12=mean(Inter_event_time12) # MIT=24 hours # data24= read.table("result_of_rainfall_duration_driedperiod_24(produce_runoff).tx t",header=FALSE) n=length(data24[,1]) #number_of_events duration24=data24[,2] dur24_mean=mean(duration24) raindepth24=data24[,1] n=length(data24[,1]) #number_of_events raindept h24_mean=mean(raindepth24) raindepth24_vars=var(raindepth24) raindepth24_sd=sd(raindepth24) raindepth24_skew=skew(raindepth24) Inter_event_time24=data24[,3] Ave_inter_event_time24=mean(Inter_event_time24) # MIT=48 hours # data48=read.table( "result_of_rainfall_duration_driedperiod_48(produce_runoff).tx t",header=FALSE) n=length(data48[,1]) #number_of_events duration48=data48[,2]

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135 dur48_mean=mean(duration48) raindepth48=data48[,1] n=length(data48[,1]) #number_of_events raindepth48_mean=me an(raindepth48) raindepth48_vars=var(raindepth48) raindepth48_sd=sd(raindepth48) raindepth48_skew=skew(raindepth48) Inter_event_time48=data48[,3] Ave_inter_event_time48=mean(Inter_event_time48) mdat < matrix(c(raindepth6_mean,raindepth12_mean,raindepth24_mean,raindepth48_m ean, raindepth6_sd,raindepth12_sd,raindepth24_sd,raindepth48_sd, raindepth6_skew,raindepth12_skew,raindepth24_skew,raindepth48_skew, Ave_inter_event_time6,Ave_inter_event_time12,Ave_inter_event_time24,Ave_int er_event_time48), nrow = 4, ncol=4, byrow=TRUE, dimnames = list(c("Average Depth(inch)", "Standard Deviation(inch)", "Skewness Coef","Intervent time(hour)"), c("6 hr", "12 hr", "24 hr","48 hr"))) mdat write(t(mdat), file="average_rainfall.txt",ncol=4,sep=" \ t") ########################### THE EN D OF PROCEDURE I ############

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136 ############################################################### #PROCEDURE II:CHOOSING THE BEST FITTED MODEL FOR RAINFALL DATA# ############################################################### ##### Step 1: Fitting distributions to rainfall data library(MASS) par(mfrow=c(1,2)) #Dm=0.44 data=matrix(scan(" Rainfall Denver MIT 12 hr .txt"),ncol=3,byrow=T) MIT data1=c(data[,1]) rainfall_depth12= data1 N=length(rainfall_depth12) #number of data points. sum_d=sum(rainfall_depth12) Ave_depth=sum_d/N Ave_depth Rainfall_duration12=c(data[,2]) sum_du=sum(Rainfall_duration12) Ave_du=sum_du/N Ave_du Rainfall_dried_period12=c(data[,3]) sum_dried= sum(Rainfall_dried_period12) Ave_dried_period=sum_dried/N Ave_dried_period

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137 boxplot (rainfall_depth12,ylab="Rainfall depth (inch)",main=" Boxplot") hist(rainfall_depth12,ylab="Number of event",xlab="Rainfall depth (inch)",main="Rainfall distribution") b ox() #To create relative frequency histograms, use the optional argument prob=TRUE.and add lines to histogram par(mfrow=c(1,1)) xl=0 xu=max(rainfall_depth12) hist(rainfall_depth12,prob=TRUE,breaks=35,col="gray",ylim=c(0,3.5),ylab="Freq uency",xlab="Rainfall depth (inch)",main="Histogram and Density Plot") box() lines(density(rainfall_depth12,from=xl,to=xu),col="black",lwd=2) #add line to histogram #legend(2, 3 .0, c("Histogram","Density estimate"),fill = c("gray","black")) legend(2, 2.0, "Density estimate",lty=1, lwd=2, merge = TRUE, bg = 'white') #plot(density(rainfall_depth12),ylim=c(0,3),xlab="Rainfall depth (inch)",col="black",lwd=2,main="Denver, Colorado" ) #box() #points at which to estimate the PDF from the simulations and the observed xeval=seq(xl,xu,length=100) neval=length(xeval) ## which distribution will fit: lognormal,Gamma,Weibull or exponential #lognormal zlog=fitdistr(rainfall_depth12,"log normal") log_densityorig=dlnorm(xeval,meanlog=mean(log(rainfall_depth12)), sdlog=sd(log(rainfall_depth12)))

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138 #logLik(zlog) #plot(log_densityorig,type="p") # Gamma zgamma=fitdistr(rainfall_depth12,"gamma") gamma_densityorig=dgamma( xeval,shape=zgamma$estimate[1],scale=1/zgam ma$estimate[2]) #plot(gamma_densityorig,type="l") # Weibull zweibull=fitdistr(rainfall_depth12,"weibull") weibull_densityorig=dweibull(xeval,shape=zweibull$estimate[1],scale=zweibull$e stimate[2]) #plot(weibul l_densityorig,type="l") #exponential zexpo=fitdistr(rainfall_depth12,"Exponential") expo_densityorig=dexp(xeval,rate=1/mean(rainfall_depth12)) #plot(expo_densityorig,type="l") hist(rainfall_depth12,prob=TRUE,breaks=35,ylim=c(0,3.5),ylab="Frequency",col= "gray",xlab=" Rainfall Depth (inch)",main="Model Comparison") box() lines(density(rainfall_depth12,from=xl,to=xu),ylim=c(0,3.5),lwd=2,xlab=" P/Dm (Rainfall depth/Average rainfall depth)",main="Denver, Colorado") lines(xeval,log_densityorig, lwd=2, col="green") lines(xeval,weibull_densityorig, lwd=2, col="red") lines(xeval, gamma_densityorig,lwd=2, col="blue") lines(xeval, expo_densityorig,lwd=2, col="purple")

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139 legend(2.5, 2.5, c("Data","Lognormal","Weibull","Gamma","Exponential"),fill = c("Black","green","red","blue","purple")) ##### Step 2: Using AIC value to choose the best fitted model aic = c(LOG=AIC(zlog, k=2), GAM=AIC(zgamma, k=2),WEI=AIC(zweibull, k=2),EXP=AIC(zexpo,k =2)) bic = c(LOG=BIC(zlog), GAM=BIC(zgamma),WEI=BIC(zweibull),EXP=BIC(zexpo)) signif(cbind(AIC=aic, BIC=bic), 4) Best_fit=cbind(min(aic),min(bic)) Best_fit ### The model with the least AIC value will be the best fitted model ####### ###################### THE END OF PROCEDURE II ### #######

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140 ############################################################# #PROCEDURE III: DETERMINING THE DESIGN CURVE FOR THE WQCV USING THE BEST FITTED MODEL## ########################################### ################### # Note to check # Denver city # Remember check MIT= 6, 12,24,48 # Check Dm # Change M1 and S1 for optimal analysis for different drain time ############################################## library(MASS) #par(mfrow=c(1,1)) data= matrix(scan(" Rainfall Denver MIT 12 hr .txt"),ncol=3,byrow=T) MIT rainfall_depth12=c(data[,1]) N=length(rainfall_depth12) #number of data points. # m=mean(rainfall_depth12) ######################################################### # # pnorm is a command for the standard normal CDF M1=mean(log(rainfall_depth12)) S1=sd(log(rainfall_depth12)) data_Do=scan("Do 12.txt") ## "Do 12.txt" is the input file for a list of the storage basin sizes.### Do=data_Do

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141 Do[1] n=length(Do) #Dm=mean(rainfall_depth12) Dm=0.44 #data_c=scan("c.txt") #C=data_c #m=length(C) Di=0.1 #Td=12 Cv=1:7 Cv1=1:n Cv2=1:n Cv3=1:n Cv4=1:n Cv5=1:n Cv6=1:n C1=0.3;C2=0.5;C3=0.6;C4=0.7;C5=0.9;C6=1.0 for (i in 1:n) Cv1[i]=pnorm((log(Do[i]/(C1*Dm)) M1)/S1) for (i in 1:n) Cv2[i]=pnorm((log(Do[i]/(C2*Dm)) M1)/S1) for (i in 1:n) Cv3[i]=pnorm((log(Do[i]/(C3*Dm)) M1)/S1)

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142 for (i in 1:n) Cv4[i]=pnorm((log(Do[i]/(C4*Dm)) M1)/S1) for (i in 1:n) Cv5[i]= pnorm((log(Do[i]/(C5*Dm)) M1)/S1) for (i in 1:n) Cv6[i]=pnorm((log(Do[i]/(C6*Dm)) M1)/S1) for (i in 1:n) Cv=rbind(Cv,c((Do[i]/Dm),Cv1[i],Cv2[i],Cv3[i],Cv4[i],Cv5[i],Cv6[i])) nt = length(Cv[,1]) write(t(Cv[2:nt,]), file="graph12.txt", ncol=7, sep=" \ t" ) #write data to file data_draw=read.table("graph12.txt",header=FALSE) #Read data outflow=data_draw[,1] capture_rate_C1=data_draw[,2] capture_rate_C2=data_draw[,3] capture_rate_C3=data_draw[,4] capture_rate_C4=data_draw[,5] capture_rate_C5=data_draw [,6] capture_rate_C6=data_draw[,7] par(mfrow=c(1,1)) plot(outflow,capture_rate_C1,ylim=c(0.0,1),xlab="Do/Dm ( Basin size/Average rainfall depth)",ylab="RVCR",type="o",pch=4,lwd=1, col="black") lines(outflow,capture_rate_C2,type="l",lty=2,lwd=1,col="bla ck") lines(outflow,capture_rate_C3,type="o",pch = 5,lwd=1, col="black")

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143 lines(outflow,capture_rate_C4,type="o",pch = 20,lwd=1, col="black") lines(outflow,capture_rate_C5,type="l",lwd=1, col="black") lines(outflow,capture_rate_C6, type="o",pch = 1,lwd=1, col="black") legend(0.5, 0.6, c("C=0.3","C=0.5","C=0.6","C=0.7","C=0.9","C=1.0"),col = "black",text.col = "black", lty = c(1,2,1,1,1,1), pch = c(4, 1,5,20, 1,1),merge = TRUE, bg = 'white') ############## THE END OF PROCEDURE III ############ ########

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144 B1. 1 Input Format Files and Output s of the Surface Numerical Model B1. 1.1 Input File for Procedure I From the left to right, the column s are rainy time (24 hr clock: for example, 100 means at 1 .00 am 2300 means the time is at 23.00 pm), name of year m onth day and r ainfall depth in 100 th of an inch 1100 1965 1 1 1 1200 1965 1 1 3 1700 1965 1 1 1 1800 1965 1 1 3 1900 1965 1 1 2 800 1965 1 25 1 1200 1965 1 28 1 2100 1965 1 29 1 2200 1965 1 29 2 2300 1965 1 29 7 2400 1965 1 29 6 100 1965 1 30 2 200 1965 1 30 5 300 1965 1 30 6 400 1965 1 30 2 500 1965 1 30 4 600 1965 1 30 4 700 1965 1 30 2 800 1965 1 30 1 1500 1965 1 31 3 1600 1965 1 31 3 1700 1965 1 31 17 1800 1965 1 31 4 1900 1965 1 31 5 2000 1965 1 31 3 2100 1965 1 31 4 2200 1965 1 31 5 700 1965 2 7 1 800 1965 2 7 1 900 1965 2 7 1

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145 B1. 1.2 Output of the Procedure I and Input File of Procedure II The results of the procedure I are sets of rainfall events with their runoff producing rainfall depths, duration and dry period s between events for MIT=6 12 24 and 48 hr The model produces a set of rainfall events for each specific MIT. The output file of procedure I is the input file for procedure II as follows: From the left to right, the columns are the rainfall depth (inch) duration (hr) and dry period between events (hr) 0.42 12 30 0.46 11 146 0.11 8 59 0.39 31 84 0.45 15 144 0.16 13 133 0.3 36 20 0.11 15 48 0.26 28 38 0.41 53 79 0.31 8 145 0.61 37 88 0.11 3 143 0.38 7 13 0.12 15 20 1.12 49 107 2.77 20 102 0.34 2 18 0.67 4 23 0.59 5 18 0.42 5 17 2.05 6 20 0.11 2 24 0.72 22 12 0.35 4 15 0.51 26 46 0.12 2 24 0.17 4 15

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146 B1. 1.2 Output of the Procedure I I The procedure II will choose the best fitted model among the selected models such as Log normal, Weibull, Gamma, and Exponential distribution using The model with the least AIC will be selected as the best fitted. In this study, Log no rmal distribution is the best fitted model B1. 1.3 Input and Output of the Procedure III The input file for the procedure III is the same format as the input file for the procedure II. In this study, w ith a selected MIT of 12 hr the model produces the design curve for WQCV for different runoff coefficients such as 0.3, 0.5, 0.7, 0.9 and 1.0.

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147 B 2 The Microsoft Excel Spreadsheet for the Sub Surface Numerical Model Based on the steps in the flowchart of the Figure 3.5, the Spread sheet s were w ith the different cap The diameter d=1.0 in (Existing condition) and d=0.44 in (Future condition) are used to calculate as an example as shown in spreadsheets from page 143 to 144 for d=1.0 in and from 145 to 148 for d=0.44 in.

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