SIMULATING SURFACE FLOW AND SEDIMENT TRANSPORT IN VEGETATED WATERSHED FOR CURRENT AND FUTURE CLIMATE CONDITION By Yang Bai A Dissertation Submitted to the Faculty of the DEPARTMENT OF CIVIL ENGINEERING AND ENGINEERING MECHANICS In Partial Fulfillment of the Requirements For the Degree of DOCTOR OF PHILOSOPHY WITH A MAJOR IN CIVIL ENGINEERING In the Graduate College THE UNIVERSITY OF ARIZONA 2014 2 UNIVERSITY OF ARIZONA GRADUATE COLLEGE As members of the Dissertation Committee, we certify that we have read the dissertation prepared by YANG BAI entitled SIMULATING SURFACE FLOW AND SEDIMENT TRANSPORT IN VEGETATED WATERSHED FOR CURRENT AND FUTURE CLIMATE CONDITION and recommend that it be accepted as fulfilling the dissertation requirement for the Degree of DOCTOR OF PHILOSOPHY _____________________________________________________________Date: April 15, 2014 Dr. Jennifer G. Duan _____________________________________________________________Date: April 15, 2014 Dr. Juan B Valdes _____________________________________________________________Date: April 15, 2014 Dr. Kevin Lansey _____________________________________________________________Date: April 15, 2014 Dr. Thomas Mexiner Final approval and acceptance of this dissertation is contingent upon the candidate’s submission of the final copies of the dissertation to the Graduate College. I hereby certify that I have read this dissertation prepared under my direction and recommend that it be accepted as fulfilling the dissertation requirement. _____________________________________________________________Date: April 15, 2014 Dissertation Director: Dr. Jennifer G. Duan 3 STATEMENT BY AUTHOR This dissertation has been submitted in partial fulfillment of requirements for an advanced degree at the University of Arizona and is deposited in the University Library to be made available to borrowers under rules of the Library. Brief quotations from this dissertation are allowable without special permission, provided that accurate acknowledgment of source is made. Requests for permission for extended quotation from or reproduction of this manuscript in whole or in part may be granted by the author. SIGNED: Yang Bai 4 ACKNOWLEDGEMENTS I would like to express my sincere gratitude to my advisor, Dr Jennifer Duan, for her valuable guidance and consistent encouragement throughout this study. Being a meticulous and creative researcher, she always points me the correct directions and teaches me how to achieve my target bit by bit. I will always be grateful for her patience and sincerity. I am equally grateful to my committee members, Dr. Juan B Valdes, Dr. Kevin Lansey and Dr. Thomas Mexiner, for their encouragement and insightful comment to my study. I am heartily thankful to my colleagues Chuanshui Yu, Jaeho Shim, Khalid A Abdalrazaak al Asadi, Shiyan Zhang, Ari Posner, Anu Acharya, Jianyin Zhou, Lei liu and alumnus Erick Rivera-Fernandea, Tongchao Nan and Eleonora Maria Demaria for all the help they offered in my study. It is a pleasant experience to work with all of them. I also thank my friends Xiaobin Ding, Rui Chen, Qiuli Shen, Fei Du, Di Wang, Xin Ren, Run Huang, Xinda Hu, Zhifeng Yan and many others. They have supported me for my life in a foreign country. In the last but not the least, I would like to express my thanks to my parents and my brother. Thanks for your love and support in every step. 5 The funding support from US National Science Foundation, Water and Climate Sustainability Program, Grant 1038938, to the University of Arizona is highly appreciated. 6 TABLE OF CONTENTS TABLE OF CONTENTS .................................................................................................... 6 LIST OF FIGURES ............................................................................................................ 9 LIST OF TABLES ............................................................................................................ 12 ABSTRACT ...................................................................................................................... 13 CHAPTER 1 INTRODUCTION ...................................................................................... 16 1.1 Statement of Problem .............................................................................................. 16 1.2 Literature Review .................................................................................................... 20 1.2.1 Numerical Modeling of Unsteady Flow and Sediment Transport for Channel Networks .................................................................................................................... 20 1.2.2 Research on Effects of Vegetation on Flow and Sediment Transport .............. 22 1.2.3 Two-dimensional Surface Routing Model ....................................................... 26 1.2.4 Prediction of Flood Frequency Curve Incorporating Climate Change ............. 27 1.3 Objective ................................................................................................................. 30 CHAPTER 2 GOVERNING EQUATIONS AND NUMERICAL METHODS .............. 32 2.1 Governing Equations for One-dimensional Flow and Sediment Model ................. 32 2.2 Governing Equations for Two-dimensional Hydrological Model .......................... 34 2.3 Numerical Methods ................................................................................................. 36 CHAPTER 3 SIMULATING UNSTEADY FLOW AND SEDIMENT TRANSPORT IN VEGETATED CHANNEL NETWORK .......................................................................... 40 3.1 Introduction ............................................................................................................. 40 3.2 Mathematical Formulation ...................................................................................... 43 3.2.1 Governing Equations ........................................................................................ 43 3.2.2 Empirical Formulae .......................................................................................... 43 3.2.3 Impacts of Vegetation on Flow Field ............................................................... 45 3.2.4 Vegetation Influence on Sediment Transport ................................................... 47 3.2.5 Infiltration Model ............................................................................................. 50 7 TABLE OF CONTENTS - continued 3.3 Numerical Solution Method .................................................................................... 51 3.3.1 Numerical Schemes .......................................................................................... 51 3.3.2 Boundary Conditions ........................................................................................ 51 3.4 Case Study ............................................................................................................... 53 3.4.1 Case 1: Steady Flow in Flume with Vegetation ............................................... 53 3.4.2 Case 2: 2006 Flash Flood in Santa Cruz River, Tucson, AZ............................ 58 3.5. Discussion .............................................................................................................. 66 3.5.1 Influence of Vegetation Coverage .................................................................... 67 3.5.2 Significance of Non-Equilibrium Model .......................................................... 68 3.6 Conclusions ............................................................................................................. 70 CHAPTER 4 APPLICATION OF TWO-DIMENSIONAL SURFACE ROUTING MODEL FOR SANTA CRUZ WATERSHED BY CONSIDERING VEGETATION COVERAGE INLUENCE ................................................................................................ 72 4.1 Introduction ............................................................................................................. 72 4.2 Modifications to CHRE2D Model .......................................................................... 73 4.2.1 Quantification of Vegetation Coverage ............................................................ 73 4.2.2 Incorporation of Vegetation Influence ............................................................. 73 4.2.3 Other Hydrological Processes .......................................................................... 76 4.3 Study Site and Data Source ..................................................................................... 77 4.3.1 The Study Site .................................................................................................. 77 4.3.3 Precipitation Data Source ................................................................................. 78 4.4 Model Application and Calibration ......................................................................... 79 4.5 Conclusions ............................................................................................................. 81 CHAPTER 5 IMPACTS OF CLIMATE CHANGE ON MAGNITUDE AND FREQUENCY OF FLOOD IN LOWER SANTA CRUZ RIVER ................................... 82 5.1. Introduction ............................................................................................................ 82 5.2 Watershed Description and Data Source ................................................................. 85 8 TABLE OF CONTENTS - continued 5.2.1 The Study Site .................................................................................................. 85 5.2.2 Climate Data Source ......................................................................................... 86 5.2.3 Bias Correction of Precipitation Data ............................................................... 86 5.2.4 Watershed Model .............................................................................................. 95 5.3 Results ..................................................................................................................... 95 5.3.1 Comparison of Observed and Simulated Results for Historical Period ........... 95 5.3.2 Flood Magnitude and Frequency Analysis Using Annual Maximum Data ..... 99 5.3.3 Flood Frequency Analysis Using Daily Maximum Data ............................... 102 5.4 Conclusions and Discussion .................................................................................. 104 CHAPTER 6 SUMMARY, CONCLUSIONS AND FUTURE RESEARCH................ 106 6.1 Summary and Conclusions .................................................................................... 106 6.2 Future Research ..................................................................................................... 109 REFERENCES ............................................................................................................... 111 9 LIST OF FIGURES Figure 1.1 Concept of watershed model and channel network model………….………..17 Figure 3.1 Four zones in the vertical profile for horizontal velocity…………….……....46 Figure 3.2 Sketch map for confluence point…………………………………………......52 Figure 3.3 Flow chart of the program……………………………….…………….…..…53 Figure 3.4 Flume set-up and vegetation arrangement for the experiment case………….55 Figure 3.5 Measured (t = 0h and t =13h) and calculated (t = 13h) bed levels for Run 2..56 Figure 3.6 Measured (t = 0h and t =30h) and calculated (t = 30h) bed levels for Run 2..57 Figure 3.7 Measured (t = 0h and t =14.5h) and calculated (t = 14.5h) bed levels for Run 3....…………………………………………………………………………………….….58 Figure 3.8 Measured (t = 0h and t =32h) and calculated (t = 32h) bed levels for Run 3..58 Figure 3.9 Simulation area and USGS gauge location.…………………...……………..60 Figure 3.10 Flow hydrograph in different gauges…………………………………….…61 Figure 3.11 Simulation and measured flow rate result at La Cholla, Rillito River….…..64 Figure 3.12 Simulation and measured flow rate result at Cortaro gauge, Santa Cruz River…...............................................................................................................................64 Figure 3.13 Bed elevation change along Rillito River…………………………...…..…..65 Figure 3.14 Bed elevation change along Santa Cruz River………...………………....…66 Figure 3.15 Sensitivity analysis of bed elevation change along Rillito River on vegetation density…………………………………………………………………………….….......67 Figure 3.16 Sensitivity analysis of bed elevation change along Santa Cruz River on vegetation density………………………………………………………….…………….68 Figure 3.17 Comparison of results from non-equilibrium and equilibrium model using 7 nodes and 10 nodes at t = 30 hours, respectively…………………...……………..…….70 Figure 4.1 Satellite photos coverage area………………………………………….……74 10 LIST OF FIGURES - continued Figure 4.2 Extracted vegetation layers for representative photos…………..……………75 Figure 4.3 Map of the Santa Cruz River Watershed………………………………..……78 Figure 4.4 Rainfall depth (mm) distribution at different time (t = 5, 11, 21 hours) for July 15th, 1999 flood event……………………………………………………………….…...79 Figure 4.5 Measured and simulated hydrograph for Cortaro gage of July 15th, 1999…...80 Figure 4.6 Water depth (m) at different time (t = 6, 12, 22 hours) for July 15th, 1999 flood event…………………………………………………….………………………………..81 Figure 5.1 Monthly precipitation raw data and bias-corrected data for a selected cell….89 Figure 5.2 WRF model raw and bias-corrected monthly P and monthly median precipitation P data for 1990 -2000 for a selected cell ..……………..………….………90 Figure 5.3 WRF model raw and bias-corrected monthly P and monthly median precipitation P data for 2031- 2040 for a selected cell…………………………………..90 Figure 5.4 WRF model raw and bias-corrected monthly P and monthly median precipitation P data for 2071-2079for a selected cell……………………………………91 Figure 5.5 Monthly median precipitation P raw data and bias-corrected data for different periods with spatial average……………………………………………….92 Figure 5.6 Daily precipitation (P) data for a selected cell for period 1990-2000………..93 Figure 5.7 Hourly precipitation (P) raw data and bias-corrected data (B-C) for Period 1990-2000………………………………………………………………………...94 Figure 5.8 Percent of yearly peak discharge exceeded certain discharge of observed and simulated data for 1990-2000 periods ……………………………………….…………..98 Figure 5.9 Current Log-Person III Flood frequency curves for Santa Cruz River at Cortaro using USGS 17B ………………………………………………………………..98 Figure 5.10 Percent of daily peak discharge exceeded certain discharge for observed and simulated 1990-2000 period …………………………………………………………….99 Figure 5.11 Percent of yearly peak discharge exceeded certain discharge for observed historical period and simulated future periods ……………...……………….…………101 11 LIST OF FIGURES - continued Figure 5.12 Current and future Log-Person III flood frequency curves for Santa Cruz River at Cortaro using USGS 17B …………………………………………..…………101 Figure 5.13 Percent of daily peak discharge exceeded certain discharge for observed historical period and simulated future periods ……………………...………………….104 12 LIST OF TABLES Table 1.1 List of some equations to calculate roughness coefficient……………………24 Table 3.1 Parameters used in the cases…………………………………………………..55 Table 3.2 Results related to bed form for Case 1……………………………………......57 Table 3.3 d50 and d90 of sediment samples in different locations of Santa Cruz River and Rillito River……………………………………………………………...……….……...62 Table 3.4 Errors analysis of flow hydrograph and bed elevation change………………..66 Table 4.1 Vegetation coverage for different locations…………….…………….……....75 Table 5.1 Root-mean-square-error of WRF model bias-corrected daily precipitation and observed daily precipitation for all cells…..…………………………………………......93 Table 5.2 Statistical analysis results of yearly peak flow for different periods………...102 Table 5.3 Average times of daily peak flow greater than certain discharge for one year of each period………………………………………………………………..………….....104 13 ABSTRACT The complex interaction between flow, vegetation and sediment drives the never settled changes of riverine system. Vegetation intercepts rainfall, adds resistance to surface flow, and facilitates infiltration. The magnitude and timing of flood flow are closely related to the watershed vegetation coverage. In the meantime, flood flow can transport a large amount of sediment resulting in bank erosion, channel degradation, and channel pattern change. As climate changes, future flood frequency will change with more intense rainfalls. However, the quantitative simulation of flood flow in vegetated channel and the influence of climate change on flood frequency, especially for the arid and semi-arid Southwest, remain challenges to engineers and scientists. Therefore, this research consists of two main parts: simulate unsteady flow and sediment transport in vegetated channel network, and quantify the impacts of climate change on flood frequency. A one-dimensional model for simulating flood routing and sediment transport over mobile alluvium in a vegetated channel network was developed. The modified St. Venant equations together with the governing equations for suspended sediment and bed load transport were solved simultaneously to obtain flow properties and sediment transport rate. The Godunov-type finite volume method is employed to discretize the governing equations. Then, the Exner equation was solved for bed elevation change. Since sediment transport is non-equilibrium when bed is degrading or aggrading, a 14 recovery coefficient for suspended sediment and an adaptation length for bed load transport were used to quantify the differences between equilibrium and non-equilibrium sediment transport rate. The influence of vegetation on floodplain and main channel was accounted for by adjusting resistance terms in the momentum equations for flow field. A procedure to separate the grain resistance from the total resistance was proposed and implemented to calculate sediment transport rate. The model was tested by a flume experiment case and an unprecedented flood event occurred in the Santa Cruz River, Tucson, Arizona, in July 2006. Simulated results of flow discharge and bed elevation changes showed satisfactory agreements with the measurements. The impacts of vegetation density on sediment transport and significance of non-equilibrium sediment transport model were accounted for by the model.. The two-dimensional surface flow model, called CHRE2D, was improved by considering the vegetation influence and then applied to Santa Cruz River Watershed (SCRW) in the Southern Arizona. The parameters in the CHRE2D model were calibrated by using the rainfall event in July 15th, 1999. Hourly precipitation data from a Regional Climate Model (RCM) called Weather Research and Forecasting model (WRF), for three periods, 1990-2000, 2031-2040 and 2071-2079, were used to quantify the impact of climate change on the magnitude and frequency of flood for the Santa Cruz River Watershed (SCRW) in the Southern Arizona. Precipitation outputs from RCM-WRF model were bias-corrected using observed gridded precipitation data for three periods before directly used in the watershed model. The 15 watershed model was calibrated using the rainfall event in July 15th, 1999. The calibrated watershed model was applied to SCRW to simulate surface flow routing for the selected three periods. Simulated annual and daily maximum discharges are analyzed to obtain future flood frequency curves. Results indicate that flood discharges for different return periods are increased: the discharges of 100-year and 200-year return period are increased by 3,000 and 5,000 cfs, respectively. 16 CHAPTER 1 INTRODUCTION 1.1 Statement of Problem Up to date, the interactions between flow, vegetation, and sediment transport are complicated and not well understood. In a river network (Figure 1.1), a large flood can cause severe bank erosion, channel degradation and channel pattern change, which can undermine instream structures. The vegetation-induced drag reduces flow velocity and increases flood attenuation and sediment deposition. Sediment aggradation or degradation will change river geometry, and in turns change channel conveyance. In a watershed, watershed runoff, the main source of flood, is influenced by the resistance of vegetation. On the other hand, the increased frequencies of heavy precipitation events are very likely to occur in the 21st Century as a result of higher global mean temperature (IPCC, 2007). The tendency of increased precipitation events will change the magnitude and frequency of flood and consequently influence sediment aggradation and degradation. Therefore, the study of interactions among flow, sediment transport, vegetation and impacts of climate changes on magnitude and frequency of flood are important engineering research topics. 17 Precipitation P Overland Flow Channel Flow Infiltrate I Channel network Sediment Figure 1.1 Concept of watershed model and channel network model Sediment transport is an extremely complex physical process. The movements of sediment particles are controlled by the resultant of gravity, drag force, lift force, and extra friction forces caused by collision between solid particles. In natural rivers, sediment transport is often associated with erosion/deposition; the process of erosion and deposition changes channel geometry, and can cause severe engineering and 18 environmental problems. Severe erosion can occur during the construction of roads and bridges when protective vegetation is removed and steep cut-and-fill slopes are left unprotected; such erosions can cause local scour along with serious sedimentation downstream (Julien, 2010). Different forms of vegetation are ubiquitous features in river main channels and floodplains; such vegetation can significantly influence stream flow processes. Riparian and in-stream vegetation can alter the hydraulics of main channel and floodplain flows; cause flow deceleration and deflection as well as local sediment deposition; affect river morphology; and provide aquatic habitat characterized by reduced or highly variable velocity, fine sediment deposition, and complex structural cover (Wu, 2005). For these reasons, the influence of vegetation must be considered when modeling flow and sediment transport in alluvial rivers. On the other hand, flood frequency plays an important role in the design of waterrelated structures. It is well known that the climate change will result in changed flood intensity and/or frequency. The frequent occurrences of extreme floods in recent decades have received much interest. For example, the Mississippi River Flood in 2010, and the nearly 500 year flood occurred in Rillito River, AZ in 2006. Many researches attributed those abnormalities to climate change due to carbon emissions. Studies of climate change concluded a global surface temperature warming for the next century (Griggs and Noguer, 2002; Klein Tank et al., 2002; Parker et al., 1992). It is expected that the warming climate will lead to increase in the magnitude of extreme precipitation (Arnbjerg-Nielsen, 2006; 19 Hennessy et al., 1997; Schmidli and Frei, 2005; Zhai et al., 2005) and other climate properties (e.g., snow melt) contributing to flooding across the globe. Flood frequency analysis has been a standard tool for designing flood protection structures. The most common approach is to combine basin-scale hydrologic models with climate change scenarios derived from climate model. Nowadays, flood flow generated from the rainfall-runoff models are commonly used for flood analysis in addition to historical records. Numerical modeling is the most cost effective tool for evaluating river changes under engineering modifications (e.g. restoration, construction). With the availability of high-capacity computers, numerical models have been widely used in one-dimensional, two-dimensional and three-dimensional hydrodynamic and sediment transport models. Although three-dimensional model is the best approximation to the real flows, it is too complicated and time consuming especially when sediment transport is simulated. Two dimensional models are often used for surface flow routing, dam break flow and sediment transport modeling. When simulating the fluvial processes in a long river reach for a long time, one-dimensional model is the most cost-effective tool. In this study, a one dimensional model will be developed to simulate flow and sediment transport in vegetated channel network, and a two dimensional surface routing model is employed to route projected precipitation throughout the study watershed for flood frequency analysis. 20 1.2 Literature Review This chapter provides a brief state-of-the-art review of related research on (a) onedimensional numerical modeling of unsteady flow and sediment transport, (b) effects of vegetation on flow and sediment transport, (c) numerical modeling of channel networks, (d) two-dimensional watershed model, and (e) prediction of flood frequency curve considering the impact of climate change. 1.2.1 Numerical Modeling of Unsteady Flow and Sediment Transport for Channel Networks The channel network is the focus for the interacting processes which carry water and sediment out of drainage basin, channels provide the network of routes along which water and sediment are carried out of a drainage basin. Because of the complex network topology, a one-dimensional network model may be the best choice for river network systems, particularly to simulate fluvial processes of long rivers for a long time. (Chen et al., 2011; Gunduz and Aral, 2005; Islam et al., 2005; Nguyen and Kawano, 1995; Shabayek et al., 2002; Zhu et al., 2010). The majority of one-dimensional sediment transport numerical model for channel networks uses weighted four-point finite difference scheme to discretize the governing equations (Chau and Lee, 1991; Wu et al., 2004); however, the stability of this scheme is strongly related to the weighting coefficients and friction terms (Lyn and Goodwin, 1987; Venutelli, 2002). An important concern for channel network modeling is the method to deal with flow and sediment exchange in confluence point. Flow condition and sediment transport are very complicated at confluence point; flow velocity will decrease in this point and resulting in 21 backwater; sediment will be trapped in confluence point. For explicit FVM method, mass and momentum conservation equations of confluence point will be imported to solve the governing equations. One-dimensional (1-D) modeling of sediment transport in streams has been extensively developed over the past decades and widely used in engineering applications due to its robustness and simpler structures when compared to multi-dimensional models. Steady and quasi-steady 1-D models, such as HEC-RAS (HEC 2010), HEC-6 (HEC1991), SRH-1D (BR 2010), IALLUVIAL2 (IIHR 2009) has been widely tested and applied to flow and sediment transport studies. For one-dimensional numerical models, Saint Venant equations are commonly used as the governing equations. The original Saint Venant Equations can be simplified by neglecting the high order differential terms to dynamic model for unsteady flow simulation (Toro, 2001). Moreover, the effect of the sediment transport to flow needs to be considered. Convection-diffusion equations can be used as the governing equations for sediment transport. The Saint Venant equations together with the sediment transport equations are generally accepted as the governing equations in most sediment models (Duan and Nanda, 2006; Wu, 2004; Zhang, 2011; Zhang and Duan, 2011). Most sediment transport formulae are developed for predicting equilibrium sediment transport rate in steady uniform flow, which assumes sediment transport rate equals to the transport capacity. However, when channel bed is degrading or aggrading, sediment transport rate can be great or less than the transport capacity, called non- 22 equilibrium transport (Zhang et al., 2013). To simulate the process that sediment transport rate gradually develops into the transport capacity, the adaptation length (Duc and Rodi, 2008; El kadi Abderrezzak and Paquier, 2009; Wu and Wang, 2007; Zhang et al., 2013) is often used to calibrate bed load transport; and the recovering coefficient is used for suspended sediment transport. The adaptation length is defined as the distance required for the bed load transport rate to reach equilibrium at a given flow condition (Cao et al., 2004; Wu and Wang, 2007). And the suspended load recovering coefficient is defined as the ratio of near-bed suspended sediment concentration to the depth-averaged concentration at equilibrium state (Zhang et al., 2013). The non-equilibrium sediment transport algorithm is adopted here to simulate sediment transport in unsteady flow in vegetated channel network. 1.2.2 Research on Effects of Vegetation on Flow and Sediment Transport Vegetation in rivers increases flow resistance and bank stability, improves water quality, and promotes habitat diversity, but vegetation also reduces channel conveyance. The existence of vegetation changes both flow field and sediment transport processes. The vegetation-induced drag reduces flow discharge in channels and helps in flood attenuation and sediment deposition. Open channel flows are not only resisted by boundary shear but also by the drag induced by stems and foliage. Even though the subject has been studied for decades, the simulation of flow and sediment transport in vegetated alluvial channels is still challenging because of the complex interaction among flow, vegetation, and mobile bed. 23 Many research efforts have been devoted to conducting laboratory experiments and field measurements to quantify the effects of vegetation on flow resistance and turbulence. Most of them derived empirical relations to calculate Manning’s, Darcy’s, or Chezy’s coefficients in vegetated channels with rigid beds. Early researchers (Chow, 1959; Cowan, 1956; Kouwen, 1969) found that the Manning’s coefficient varies with vegetation type, density, and distribution. Relationships between Manning’s coefficient and vegetation properties are formulated for limited vegetation types and experimental conditions. Wu (1999) investigated the variation of vegetative roughness coefficients in non-submerged and submerged flow conditions and developed a model for the drag coefficient of vegetal elements, and then he converted it into Manning’s n-value. Klopstra (2002) established an analytical model to calculate the Chezy’s coefficient for submerged vegetation as a function of vegetation height and density, stem diameter, drag coefficient, and the characteristic length of large scale turbulence. Kouwen and Unny (1973) found the drag force of flexible vegetation is smaller than that for rigid upright vegetation because of a change in vegetation morphology. Similar research results can be found in other literatures (Carollo et al., 2005; Darby, 1999b; Duan et al., 2006; James et al., 2004; Katul et al., 2002; Kim et al., 2012; Neary et al., 2012; Stephan and Gutknecht, 2002). Some of the formulas are compiled in Table 1.1. 24 Table 1.1 List of some equations to calculate roughness coefficient Researchers Formulas nr n0 0.0239( Fisher (1992) Bv ) uR nr / h Reed et al. (1995) 1 Stone and Shen (2002) f a log R d For submerged vegetation: Baptist (2007) Cr (h hv )3/2 ( g / ) ln((h hv ) / ez0 ) 1 1/ Cb2 (Cd mDhv ) / 2 g h3/2 For non-submerged vegetation: k=h Yang and Choi (2010) 2 gh C ghs h h n u ln( ) v hv h Cd hv Cr Cheng (2011) 1 ghs 2/3 h h 1 1/16 hs 3/2 g (1 )3 d hv 3/2 ( ) 4.54 g ( s ) ( ) 2CD hv h D h For non-submerged vegetation: k=h 1/3 nr , n0 = representative, bed manning’s roughness respectively( s m ); B = volumetric blockage factor; v u = mean velocity (m/s) ; R = hydraulic radius(m); = resistance factor; h = water depth(m); f = DarcyWeisbach friction factor; a = cross section shape factor; d = roughness height of vegetation; = Von Karman constant; Cr = representative Chezy coefficient; Cb = Chezy coefficient of the bed(m1/2/s); m = number of cylinders per m2 horizontal area(m-2); D = Cylinder diameter(m); g = gravity hv = vegetation height(m); Z0 =roughness height in the logarithmic velocity profile for a fully rough bed(m); hs = water depth below vegetation for submerged condition (m); Cu = velocity acceleration( m / s 2 ); calculation coefficient; When developing numerical models for open channel flows with vegetation influence, some researchers (Baptist, 2005) modified the source terms of momentum equations by importing roughness calculation equations; other researchers (Wu and Marsooli, 2012) added vegetation drag forces as additional source terms to momentum equations. Both methods accounted for the influence of vegetation by modifying source terms in the momentum equations. Actually, roughness calculation equations are based 25 on force balance, which includes vegetation properties. Therefore, these two methods are based on the some concept but expressed differently; either method can be chosen. A few laboratory and field experiments were conducted to study the effects of vegetation on sediment transport and channel morphodynamic changes. Prosser’s (1995) experiments showed upland erosion and channel initiation can be prevented by strong soil cohesion from a dense root mat. López and García (1998) derived an empirical equation from field data to estimate suspended sediment transport, and their results showed the suspended sediment transport capacities in vegetated waterways are smaller than that in non-vegetated channels. Zong and Nepf (2011) found that for a patch of vegetation located at a channel side, sediment deposition was the highest near the streamwise patch edge and decreased into the patch. Only a few numerical models (Wu and Shields, 2005) were capable of simulating both flow and sediment transport in vegetated channels. Wu and Shields (2005) developed a two-dimensional depth-averaged model to simulate flow and sediment in channels with riparian vegetation. However, there model can only be used in small scale curved channels. Shear stress in vegetated channels is composed of bed shear stress, wall shear stress and vegetation shear stress. Bed shear stress is the one works on sediment and causes the motion of sediment. When flow resistance induced by vegetation is considered, the velocity of flow decrease, resulting in the decrease of bed shear stress. If the threshold of motion of sediment is defined in terms of a critical shear stress, sediment starts to move when bed shear stress is larger than critical shear stress. So it is very important to express bed shear stress correctly when vegetation influence is considered. Although 26 some research results have been reported on vegetation influence on sediment transport as listed above, the relationship between bed shear stress and vegetation influence still needs to be investigated, and a formula for the bed shear stress in vegetated channel is not yet available. 1.2.3 Two-dimensional Surface Routing Model The response of magnitude and frequency of flood change of natural watershed to climate depends on the mechanisms of runoff generation and their spatial and temporal distribution (Vivoni, et al., 2007). Many distributed surface flow routing models have been developed to represent the runoff response to varying watershed properties. The distributed surface flow routing includes two components: overland flow routing and channel flow routing. Two kinds of procedures are used to simulate surface flow routing. Some researchers used two models for overland and channel flow (Julien, et al., 1995; Qu and Duffy, 2007) separately. The channel network with reach cross section information and confluence point information are obtained, and then coupled with the overland model. The disadvantage of this kind of model is the difficulties of data processing. Other researches use one model to simulate both overland and channel flow (Cea, et al., 2010; Kim, et al., 2012). Nearly all the rainfall-runoff models for predicting surface flows are simply based on the solutions of simplified shallow water equations such as kinematic wave equation (Vivoni et al., 2007; Yang et al., 1998) or diffusion wave equation(Qu and Duffy, 2007). Current research(Yu and Duan, 2014) showed that the accuracy of simplified models are not enough because the neglected terms in kinematic or diffusion wave equation are significant in predicting flood peak discharge. An advanced 2D 27 hydrodynamic and sediment model, CHRE2D, has been developed in our research group by Yu and Duan (2013), Yu and Duan (2014). CHRE2D solved the surface flow using fully two-dimensional shallow water equations. The CHRE2D model is a stable model by dividing the computational domain into the shallow water zone and the kinematic wave zone. An approximate solution based on the kinematic wave equation is applied to the kinematic wave zone. The CHRE2D model was used in this study. 1.2.4 Prediction of Flood Frequency Curve Incorporating Climate Change In the last decade, the interest in the impacts of climate change on river flows is increasing. Interagency Panel on Climate Change (IPCC) (2007) found that climate change will drive changes in magnitude and frequency of flood. The effect of climate change on river flows has been studied on different spatial locations for various future time periods using time series of climate model projected data. The most common procedure to model the effect of climate change on river discharge is achieved by routing the precipitation generated from a climate model using a basin-scale hydrologic model. For examples, researches for river basins in the USA include Christensen et al., (2004), Murphy and Ellis (2014), in Belgium (Goderniaux et al., 2009), in Australia (Leonard et al., 2008), in Netherlands (Leander et al., 2008), in Denmark (Madsen et al., 2009), in United Kingdom (Fowler and Kilsby, 2007; Kay et al., 2006b), in China (Cong et al., 2009) and et al. . The first requirement for accounting for the impact of climate change on flow discharge is a reliable estimation of climate change for a given future period. Changes in 28 extreme precipitations directly impact the hydrological processes, consequently the frequency and magnitude of flood. Although precipitations from the global climate models (GCMs) were used in several studies (Cameron et al., 1999; Merritt et al., 2006), GCMs generally do not realistically represent precipitation because of the coarse spatial resolution and physical parameterizations, especially for complex terrain. Downscaling has to be performed for regional assessment. The dynamically downscaled method, the regional climate model (RCM) nested inside the GCM, increases the spatial resolution and gives a better representation of precipitation. RCMs can capture mean and extreme precipitation at the regional scale (Dominguez et al., 2012). To date, several researches have applied the daily or monthly precipitation extremes from the RCM model to estimate the change of flood magnitude and frequency (Bell et al., 2007; Fowler and Kilsby, 2007; Hailegeorgis et al., 2013; Hay et al., 2002; Wang et al., 2013). However, Hanel and Buishand (2010) found the increase in the large quantiles of daily maxima was much smaller than that in the quantiles of the hourly maxima at the end of the 21st century based on the transient RCM simulations. Because of this, the hourly precipitation data from RCM is used in this study for predicting the future flood magnitude and frequency. The dynamic downscaling leads to significant advantage to the data from GCM, which provides precipitation projections at a scale matching the requirement of catchment scale simulation. However, even with the fine spatial resolution, biases in the precipitation output need to be corrected (Johnson and Sharma, 2011). Bias correction methods are designed to address known biases associated with the climate outputs for the 29 region being modeled. Several bias correction methods in the literature were applied to the daily or monthly averaged data series (Hagemann et al.,2011; Piani et al., 2010; Yang et al., 2005; Wood et al. 2004). For example, Wood et al. (2004) performed a bias correction technique based on termed quantile mapping at monthly scale and disaggregated to daily scale. This study adapted the same quantile mapping method for monthly averaged precipitation, and then applied a further disaggregation step to hourly precipitation. The second requirement for predicting the impact of climate change on flow discharge is an accurate and robust hydrological model. A physically based approach that routes rainfall over realistic watershed is superior to a lumped parameter hydrologic model. One example of lumped parameter model is to use the intensity–duration– frequency (IDF) curves to derive flood frequency curve (Bloschl and Sivapalan, 1997; Goel etal., 2000). Another example involves the generation of synthetic meteorological time series as input to a rainfall–runoff model (Wilks, 1998; Lamb, 1999) to derive discharge series. Those analytical methods are based on assumptions of uniform terrain slopes, time of concentration. On the other hand, a hydrodynamic model can route projected precipitation over watershed at fine grid cells. This will allow the accurate determination of flood duration and peak flow than an analytical model. Therefore, a physical based distributed surface flow routing model for irregular terrains, CHRE2D, was selected in this study. Details regarding CHRE2D will be introduced in the following sections. 30 1.3 Objective The main objective of this research is to simulate unsteady flow and sediment transport in a vegetated channel network and predict future flood magnitude and frequency considering the change of climate. In order to achieve this objective, the following specific tasks are completed: Simulate unsteady flow and sediment transport in a channel network. 1D unsteady flow and sediment transport model developed by Zhang et al. (2013) was extended for channel network applications. This feature is essential for simulating flood routing in the arid and semi-arid Southwest US because tributary flows can dominant the main flow. The improved model is applied to the lower Santa Cruz River. Incorporate the effect of vegetation on sediment transport into the developed channel network model. A lot of research results of vegetation influence for flow dynamics and erosion/sedimentation can be found in literatures. The influence of vegetation in flow field and sediment field need to be investigated. In this research, vegetation influence need to be injected into the unsteady flow and sediment transport model by modifying source term in momentum equation; the relationship between vegetation features and shear stress need to be investigated; vegetation involved shear stress is required to be expressed in the model. Improve the CHRE2D model by considering vegetation impacts and apply the model to SCRW. Vegetation coverage analysis for SCRW is based on satellite photos. Friction terms in the momentum equations of CHRE2D are modified by 31 addressing the vegetation coverage. The improved model was calibrated using an observed flood event. Analyze the possible flood magnitude and frequency changes caused by climate change in the SCRW. The precipitation data generated from the WRF (Weather Research and Forecasting)-RCM was routed through the watershed by using the CHRE2D model. Three periods were simulated: the historical period of 19902000, the future periods of 2031-2040 and 2071-2079. In particular, we applied quantile-based mapping bias correction method to all three periods, compared the simulated stream flow for the historical (1990-2000) period with observations, and developed new flood frequency curves based on climate projected precipitations. 32 CHAPTER 2 GOVERNING EQUATIONS AND NUMERICAL METHODS The shallow water equations are derived from depth-integrating the Navier-Stokes equations, in the case where the horizontal length scale is much greater than the vertical length scale. Situations where the horizontal length scale is much larger than the vertical length scale are common, so the shallow water equations are widely used in open channel modeling, surface routing modeling, atmospheric and oceanic modeling. The shallow water equations can be further simplified to the commonly used one-dimensional Saint Venant equation which is widely applied for dam break simulation, open channel modeling, as well as storm runoff in overland flow. The shallow water equations are used as governing equations for the two-dimensional hydrological model and the onedimensional Saint Venant equation is used for one-dimensional unsteady flow and sediment transport model. The Godunov-type finite volume method is used to discretize the governing equations. 2.1 Governing Equations for One-dimensional Flow and Sediment Model The governing equations are the St. Venant equations modified by treating the density of sediment laden flow as a variable, as well as mass conservation equations for suspended load and bed load (Zhang and Duan, 2011) written as: 33 A Q b Ab 0 t x t (2.1) n 2Q Q zs 1 Q2 gAh g 0 Q gA 4 t x A x 2 x AR 3 (2.2) AC QC BE D t x Qb t u b Qb 1 Q*b Qb L x (2.3) (2.4) where t=time; x = longitudinal coordinate; A = flow area; Q = flow discharge; Ab = mobile bed area; g = gravitational acceleration; z s = water surface elevation; n = Manning’s roughness; R = hydraulic radius; C = concentration of suspended load; B = width of the cross section; E = entrainment rate at the interface between bed load and suspended load; D = deposition rate at the interface between bed load and suspended load; L = non-equilibrium adaptation length; Q*b = bed load transport capacity under equilibrium state; Qb = actual bed load transport rate; = density of the water-sediment mixture, where w 1 Ct s Ct , where w and s are the density of the water and sediment, respectively, and C t the volumetric concentration of total load sediment, calculated as Ct C Qb ; Q b = density of mobile bed layer, calculated as b w pm s 1 pm , with p m being the porosity of bed load sediment; h = averaged flow depth in a cross section, equivalent to the local flow depth in a rectangular flume. Eq. (2.1) and (2.2) are the St. Venant equations for sediment laden flow over alluvial bed, and 34 Eq. (2.3) and (2.4) are mass conservation equations for bed load and suspended load, respectively. Bed elevation change is calculated by solving the Exner equation for bed surface layer, which is written as 1 pm Ab 1 BD E Qb Qb* t L (2.5) where Ab = mobile bed area; Q*b = bed load transport capacity under equilibrium state; Qb = actual bed load transport rate, p m = the porosity of bed load sediment. 2.2 Governing Equations for Two-dimensional Hydrological Model The governing equations used in CHRE2D are the two-dimensional depthaveraged shallow water equations (Fraccarollo and Toro, 1995; Garcia-Navarro et al., 1995; Zhao et al., 1994), which can be written in the differential conservative form as: Q F G Ss Sf Sr t x y (2.6) where Q is the vector of conservative variables; F and G are the vectors of advective fluxes in x and y directions, respectively; S s is the vector of bed slope source term; S f is the vector of bed friction source term; S r is the vector of rainfall excess source term. The vector of primitive variables, U , and the vector of conservative variables, Q , in Eq. (2.6) are defined as: 35 h h U u , Q hu v hv where h is flow depth; u and v (2.7) are the depth-averaged flow velocities in x and y directions, respectively. The vectors of advective fluxes, F and G , are given as: hu hv 2 2 F hu gh / 2 , G hvu hv 2 gh 2 / 2 huv (2.8) where g is the gravity acceleration. The source terms, including bed slope, bed friction, and rainfall excess, are calculated by: 0 0 i0 C u u Ss ghS0 x , Sf f , Sr 0 0 C u v ghS0 y f where S0 x b b and S0 y are the bed slopes in x y x (2.9) and y directions, receptively; b is bed elevation; C f gn2 h1/3 is drag coefficient; n is Manning’s roughness coefficient; u u 2 v 2 ; and i0 is the rainfall excess rate. The kinematic wave approximation (KWA) is used in CHRE2D model when water depths are thin. For flow condition with thin water depth, the local acceleration and advective terms in the momentum equations are insignificant compared to the friction and the bed slope source terms and the momentum equations of Eq. (2.6) are simplified to: 36 Ss Sf (2.10) From Eq. (2.8), the depth-averaged flow velocities are calculated as: h 4/3 u u S 0 x n2 4/3 v u S h 0y n2 (2.11) 2.3 Numerical Methods The Godunov-type finite volume method is applied to discretize the governing equations for both one-dimensional unsteady flow and sediment model and twodimensional hydrological model. For one-dimensional model, the density of sediment laden flow can be expressed as w 1 Ct s Ct for suspended sediment layer and b w 1 pm s pm for bed load layer. If only the suspended load is being simulated, or the bed load transport velocity is close to the flow velocity, Eq.(2.1) to(2. 4) can be reformulated as: A Q 1 t x 1 p m Q Q 2 t x A 1 Qb* Qb BD E L0 QQ z 1 gA s gAh p gn 2 4 x 2 x AR 3 Ct 1 Q s w 1 Qb* Qb BD E A w 1 p m L AC QC BE D t x (2.12) (2.13) (2.14) 37 Qb t u b Qb 1 Qb* Qb L0 x (2.15) Eq. (2.12) to (2.15) can be re-written (Zhang and Duan, 2011)in the vector form as follows: F S x t (2.16) where Q A 2 Q , F Q QC AC Qb Qb U b 1 1 Qb* Qb BD E 1 p m L0 Q Q Q s w z s 1 2 4 S () gA x 2 gAh p x gn AR 3 A w B( E D) 1 (Q*b Qb ) L A , Ct 1 1 Qb* Qb BD E 1 p m L (2.17) (2.18) where S are the source terms for Eq. (2.1) – (2.4), respectively. The Godunov-type finite volume method (Toro, 2001) evaluates the value of at time n+1 using the value at time n: in1 in t n F 1 F n 1 t S i x i 2 2 where subscript i represents the node, subscript i (2.19) 1 represents the east or the west cell 2 face, superscript n and n+1 present the current and the future time level, respectively; t = time step; x distance between two cross sections; F = intercell numerical flux at the 38 cell face; S = source terms. The upwind numerical scheme is implemented, and written in a general form as seen in (Zhang and Duan, 2011) and (Ying et al., 2004): F i 1 2 Qin k n 2 n A Q ni k n i k Qi k C i k Q n b ik (2.20) Where k = 0 if Qi 0 and Qi 1 0 ; k=1 if Qi 0 and Qi 1 0 ; k=1/2 otherwise. The shallow water equations are also discretized by the Godunov-type finite volume method (LeVeque, 2002; Toro, 2009) over a regular Cartesian mesh. Using the explicit Euler scheme for the temporal derivative term, the discretized form of the governing equations can be written as: Q( n 1) Q( n ) t 4 Fj (Q(Ln ) , Q(Rn ) ) n j L j t (S(0n ) S(fn ) S(rn ) ) A j 1 (2.21) where superscript ( n ) and (n 1) refer to the variables at current and next time step; t is time step; A is the cell area; j is the index of a cell edge; Fj (Q L , Q R ) is the vector of Riemann flux calculated by solving a local Riemann problem normal to the edge j ; Q L and Q R are the vectors of conservative variables on the left and right side of the edge j ; n j is the normal vector to the edge j ; L j is the length of the edge j . The local Riemann problem is solved by the Harten-Lax-van Leer (HLL) approximate Riemann solver (Harten, 1984; Toro, 2001). The flux across the cell interface is calculated by: 39 F(Q L ), if sL 0 * F(Q L , Q R ) F (Q L , Q R ), if sL 0 sR F(Q ), if sR 0 R (2.22) * where the flux vector at the star region F (QL , QR ) is determined by: F* (QL , QR ) sR F(QL ) sLF(QR ) sL sR (QR QL ) sR sL (2.23) The left wave speed, sL , and, the right wave speed, sR , are estimated by: sL min(uLn ghL , us cs ) n sR max(uR ghR , us cs ) (2.24) n n where uL and uR are normal velocities at the left and the right side of the cell interface; us and cs are defined as: us (uLn uRn ) / 2 ( ghL ghR ) n n cs (uL uR ) / 4 ( ghL ghR ) / 2 (2.25) For the dry bed situation, the estimated wave speeds are replaced by the exact dry front speed (Causon, et al., 2000; Toro, 2001) as: sL uLn ghL right dry bed: n sR uR 2 ghL left dry bed: sL uRn 2 ghR n sR uR ghR (2.26) 40 CHAPTER 3 SIMULATING UNSTEADY FLOW AND SEDIMENT TRANSPORT IN VEGETATED CHANNEL NETWORK 3.1 Introduction Vegetation in natural rivers increases flow resistance and bank stability, improves water quality, and promotes habitat diversity, but reduces flood conveyance. The presence of vegetation changes both flow field and sediment transport processes. Although the impact of vegetation on flow and sediment transport has been studied for decades (Cowan, 1956; Duan et al., 2006; Fisher, 1992; Luhar and Nepf, 2013; Nepf, 2012; Tsujimoto, 1999), the simulation of flow and sediment transport in vegetated alluvial channels is still challenging because of the complex interactions among flow, vegetation, and mobile bed sediment. Many empirical relations have been proposed to quantify the resistance of vegetated flow over a rigid bed through adjusting Manning’s, Darcy’s, or Chezy’s coefficients. Early researchers (Chow, 1959; Cowan, 1956; Kouwen, 1969) found that the Manning’s coefficient varies with vegetation type, density, and distribution. Relationships between Manning’s coefficient and vegetation properties are formulated for limited vegetation types and experimental conditions. Klopstra (2002) established an analytical model to calculate the Chezy’s coefficient for submerged vegetation as a function of vegetation height and density, stem diameter, drag coefficient, and the characteristic length of large scale turbulence. Kouwen and Unny (1973) found the drag 41 force of flexible vegetation is smaller than that for rigid upright vegetation because of a change in vegetation morphology. Similar research results can be found in other literatures (Carollo et al., 2005; Darby, 1999b; Duan et al., 2006; James et al., 2004; Katul et al., 2002; Kim et al., 2012; Neary et al., 2012; Stephan and Gutknecht, 2002). To simulate vegetated open channel flow using numerical models, some researchers (Baptist, 2005) modified source terms in the momentum equations by incorporating an equation for calculating the roughness; other researchers (Stone and Shen, 2002; Wu and Marsooli, 2012) added vegetation drag forces to the momentum equations as additional source terms. Both methods accounted for the influence of vegetation by modifying source terms in the momentum equations. A few laboratory and field experiments were conducted to study the effects of vegetation on sediment transport and channel morphodynamic changes. Prosser’s (1995) experiments showed upland erosion and channel initiation can be prevented by strong soil cohesion from a dense root mat. López and García (1998) derived an empirical equation from field data to estimate suspended sediment transport, and their results showed the suspended sediment transport capacities in vegetated waterways are smaller than that in non-vegetated channels. Zong and Nepf (2011) found that for a patch of vegetation located at a channel side, sediment deposition was the highest near the streamwise patch edge and decreased into the patch. Only a few numerical models (Wu and Shields, 2005) were capable of simulating both flow and sediment transport in vegetated channels. Wu and Shields (2005) developed a two-dimensional depth-averaged model to simulate flow 42 and sediment in channels with riparian vegetation. However, there model can only be used in small scale curved channels. Most sediment transport formulae are developed for predicting equilibrium sediment transport rate in steady uniform flow, which assumes sediment transport rate is equal to the transport capacity. However, when channel bed is degrading or aggrading, sediment transport rate can be greater or less than the transport capacity, called nonequilibrium transport (Zhang et al., 2013). To simulate the process that sediment transport rate gradually develops into the transport capacity, the adaptation length (Duc and Rodi, 2008; El kadi Abderrezzak and Paquier, 2009; Wu and Wang, 2007; Zhang et al., 2013) is often used to calibrate bed load transport, and the recovering coefficient is used for suspended sediment transport. The adaptation length is defined as the distance required for the bed load transport rate to reach equilibrium at a given flow condition. And the suspended load recovering coefficient is defined as the ratio of near-bed suspended sediment concentration to the depth-averaged concentration at equilibrium state (Zhang et al., 2013). The non-equilibrium sediment transport algorithm is adopted here to simulate sediment transport in vegetated channel network. Although 2D and 3D models have been developed to simulate flow and sediment transport in vegetated channels (Wu, 2005), 1D channel network model is the most costeffective for engineering practices when simulating fluvial processes of a long river reach for a long time. In this chapter, a one-dimensional model for simulating unsteady flow and sediment transport in a vegetated channel network will be presented. The model 43 accounts for the effect of vegetation on flow resistance and sediment transport by using the modified roughness coefficient and shear velocity. A laboratory experimental case and an unsteady flow event occurred in the Santa Cruz River, Tucson, AZ were used to verify the model. The governing equations, numerical methods and application of the developed model are presented in the following sections. 3.2 Mathematical Formulation 3.2.1 Governing Equations The one-dimensional St. Venant equations were described in Chapter 2. 3.2.2 Empirical Formulae To close the model, additional empirical sediment transport formulae are required. Sediment deposition (D) and entrainment rates (E) at the interface between bed-load and suspended-load layers are defined as follows: D s Ca (3.1) E s Ca* (3.2) in which ws = settling velocity of sediment particles; Ca * = the concentration at the interface at equilibrium; Ca is the actual suspended sediment concentration at the interface, it is related to the depth averaged concentration of suspended load as Ca C , in which = the ratio of the near-bed concentration to the mean concentration of the suspended sediment at a cross section, also defined as the non-equilibrium suspended 44 load recovery coefficient. The suspended load recovery coefficient, , was calculated from the modified Rouse profile as (Zhang et al., 2013): h (3.3) h z a a z h a dz R0 h u*' (1 / ) [1 ( E / D 1)] / [ ( E / D 1)] s R0 1 / if s u*' if s u*' (3.4) in which z = elevation; a = reference bed level; u*' = grain shear velocity; R0 = Rouse number; = correction factor, approximately equal to 1.0; = Von Karman constant, 0.41. The adaptation length for non-equilibrium bed load transport, L , is a function of the dominant bed forms and channel geometry , which is equivalent to the length of sand dunes, approximately 5-10 times the flow depth (Wu and Wang, 2007). The empirical formulae proposed by Van Rijn (1984a,b) were used to determine the bed-load transport capacity, Qb* , and the suspended-load near-bed concentration, Ca* , at the equilibrium state presented as Eq. 3.5 and Eq. 3.6. Qb* 0.053 T 2.1 0.5 1.5 ( s 1) g d50 2.1 D* Ca* 0.015 d50 T 1.5 a D*0.3 where T = transport stage parameter; D* = particle parameter; s = specific density. (3.5) (3.6) 45 3.2.3 Impacts of Vegetation on Flow Field The increase of flow resistance due to vegetation can be quantified by several hydraulic roughness coefficients. The most commonly used are the Manning roughness coefficient (n), the Chezy resistance factor (CR), and the Darcy-Weisbach friction factor (f) (Kim et al., 2012). Because of the increase of flow resistance, the vertical distribution of time-averaged velocity doesn’t satisfy the logarithmic law in vegetated channels. A typical velocity profile for submerged vegetation is shown in Figure 3.1 (Baptist, 2007), in which velocity in vegetated zone is nearly a constant. Several laboratory and field experimental studies have correlated vegetation characteristics with roughness coefficients. Darby (1999a) derived a Darcy-Weisbach friction factor for both flexible and nonflexible vegetation. Baptist (2007) suggested an analytical equation to calculate the Chezy coefficient for un-submerged vegetation. He also derived an effective flow depth method for submerged vegetation. Yang and Choi (2010) developed a two-layer model for submerged vegetation, additional drag force terms are added to the momentum equation for each layer. Nepf (2012) proposed an equation for calculating vegetated channel resistance coefficient from the analytical solution of momentum equation. 46 h Z (m) 4 hv 3 dz 2 1 u (m/s) Figure 3.1 Four zones in the vertical profile for horizontal velocity, u(z), through and over vegetation, where h = water depth, k = vegetation height, d = zero-plane displacement. (Baptist, 2007) Recently, Cheng (2011) derived resistance coefficients for both rigid and flexible vegetation by employing the concept of hydraulic radius. Cheng (2011) found his formulae can improve the roughness predictions for both rigid and flexible vegetation comparing to several existing formulas. Therefore, Cheng’s (2011) method was used to calculate Manning’s coefficient in this paper. The vegetation-related hydraulic radius is defined as: Rv 1 d 4 (3.7) where Rv = vegetation-related hydraulic radius; = vegetation density (defined as the fraction of the bed area occupied by vegetation); d = stem diameter. The Chezy coefficient for submerged vegetation is given as: 47 CR g (1 )3 d hv 2CD hv h 3/2 h 1 4.54 g s d 1/16 hs h 3/2 (3.8) where CD 130 0.8 Rv0.85 * Rv* 1 exp 400 (3.9) with CD = drag coefficient; Rv* ( g s / 2 )1/3 rv ; h = flow depth; hv = vegetation height; hs = flow depth over vegetation layer (upper layer), hs h hv ; = kinematic viscosity of fluid; s = energy slope. For emerged vegetation, hs =0 and hv h , then Eq.(3.8) is simplified as: CR g (1 )3 d 2CD h (3.10) 1/6 The Manning coefficient can be calculated as n h / CR . 3.2.4 Vegetation Influence on Sediment Transport The presence of vegetation reduces the grain resistance that transports sediment. No equation in literature is valid for separating the grain resistance for sediment transport from the total bed shear stress in vegetated channels. In the following sections, we derived an analytical equation for calculating the grain resistance from the total resistance. Considering a control volume of unit length, the resistance forces in the streamwise direction are wall shear stress, bed shear stress including grain resistance and form resistance, and vegetation drag. The sum of the three resistance forces are the total resistance force, 48 Ft Fw Fb FD (3.11) where Ft is the total resistance force; Fw , Fb and FD are the wall friction force, bed resistance force and vegetation drag force, respectively. For steady uniform flow, the total resistance force is equal to the downslope component of gravity force, and can be expressed as gsRt Pt ; the wall shear can be expressed as gsRw Pw , and bed shear as gsRb Pb , in which Pt Pw Pb Pv is the total wetted perimeter; Rt bh(1 ) / Pt is the total hydraulic radius. Pw ( 2h) and Rw are wall-related wetted perimeter and hydraulic radius, respectively; Pb [ (1 ) B] and Rb are bed-related wetted perimeter and hydraulic radius, respectively; Pv Bh / ( d / 4) and Rv are vegetation-related wetted perimeter and hydraulic radius, respectively. The vegetation drag force in the streamwise direction for emerged vegetation is (Kothyari et al., 2009): FD CD hd uv 2 2 (3.12) where ρ is fluid density; uv is average velocity of the flow among vegetation stems and can be expressed as (Cheng, 2011): uv 2 gRv s CD (3.13) For submerged vegetation, h will be replaced by vegetation height as hv ; and uv will be the mean velocity of vegetation layer which can be also calculated by Eq.(3.13). Substituting equation (3.12) into equation (3.11), it yields: gsPR t t gsPw Rw gsPb Rb CD hd uv 2 2 (3.14) 49 With Pw , Pb and Pv given above, the total hydraulic radius can be determined as Cheng and Nguyen (2010): 1 1 1 Rt h 0.5B(1 ) Rv 1 (3.15) in which Rv d (1 ) / (4 ) . The Darcy’s roughness coefficient for side wall can be calculated as f w 8gRw s / uv 2 , and Rw f wuv 2 / 8gs , in which f w is wall-related Darcy-Weisbach friction factor. Applying the explicit form of the revised Colebrook equation (Cheng 2010), f w f ws f wr in which f ws Re 31 ln 1.3 f 2.7 (3.16) ; f wr 11.7 ln 7.6 4 Rt fksw 2.5 ; 2 4 Rt fk sw 0.1 ; f ws is smooth- sidewall friction factor; f wr is rough-sidewall friction factor; f 8gRt s / uv 2 is total friction factor; Re is Reynolds number; k sw is the equivalent wall-roughness height. Substituting the expressions of Pw , Pb , Rt , Rw to Eq. (3.14), yields Rb PR C hduv 2 t t Pw Rw D Pb 2 gspb (3.17) If vegetation is submerged, water depth needs to be replaced by vegetation height in Eq. (3.17). The effective grain-shear velocity equation derived by Van Rijn (1984a), which removes bed form resistance from bed resistance, was used to calculate bed-load transport capacity. The shear velocity due to grain resistance can be expressed as: 50 u*' u (3.18) 12Rb 5.75 log 3d 90 ' where u* = shear velocity due to grain resistance, u =mean velocity, d90 = size of sediment for which 90% of sediment is finer. Once u*' is determined, bed-load transport capacity Qb* can be calculated through Van Rijn (1984a). 3.2.5 Infiltration Model Abundant vegetation on the floodplain of natural waterways increases flow resistance and reduces flow velocity, and consequently increases the opportunity time for infiltration. Because of this, the infiltration need to be considered in the model, and the Green and Ampt model was used for calculating infiltration (Bras, 1990): H f Md d f K s 1 Df (3.19) in which d f = infiltration rate; Ks = saturated hydraulic conductivity; Hf = capillary pressure head at the wetting front; Md = soil moisture deficit, defined as Md = (e i ) , e = effective porosity, i = soil initial moisture content; D f = accumulated infiltrated depth. 51 3.3 Numerical Solution Method 3.3.1 Numerical Schemes The Godunov-type finite volume method is used to discretize the governing equations as shown in Chapter 2. A simplified time-explicit solution to the Green-Ampt equation was proposed by Li et al. (1976) as follows: d f i n 1 1 P1i ( P1i2 8P2i t )1/2 2t (3.20) in which subscript i represents the node; P1 and P2 are variables which can be written as P1 K s t 2D f n and P2 Ks D f n Ks H f M d ; D f ( d f t ) is the accumulated depth of infiltration, defined as the volume of water infiltrated per unit area. Water depth is updated every time step after the infiltration depth is calculated. Then, an updated cross section area is used for the calculation in the next time step. 3.3.2 Boundary Conditions The upstream boundary condition is flow hydrograph, and the downstream boundary condition is the discharge stage rating curve. At the river confluences as shown in Figure 3.2, three additional boundary conditions are needed to close the solutions. Assuming cross section 1, 2 and 3 are the confluence cross sections for each reach, the mass conservation equation, Eq. (3.21), needs to be satisfied, and the water surface elevations should satisfy Eq.(3.22) as follows: Q1 Q2 Q 3 (3.21) 52 Z s1 Z s 2 Z s 3 (3.22) in which Q1 , Q2 , Q3 , Z s1 , Z s 2 , and Z s 3 are flow discharges and water surface elevations at Section 1, 2, and 3, respectively. To solve Eq. (3.21) and (3.22), water surface elevation at the confluence was assumed, and then used as the downstream boundary condition for Reach 1 and 2, respectively. Flow discharges for these two reaches were solved from Eqs. (2.1) to (2.4). For Reach 3, flow discharge can be obtained from Eq.(3.21), and water surface elevation at the upstream section was solved from Eq. (2.1) to (2.4). If the solved water surface elevation at Reach 3 doesn’t satisfy Eq. (3.22), a correction to the guessed water surface elevation will be made until the solved water surface elevation at Reach 3 satisfies Eq. (3.22). Confluence cross section Reach 1 CS 1 CS 3 Reach 3 CS 2 Reach 2 Figure 3.2 Sketch map for confluence point The program language is FORTRAN 90, Figure 3.3 is the program flow chart. The model runs on a dual-core personal computer. 53 Start Input(Initialization and boundary condition) Calculate C’ Calculate τb*’ Calculate A, Q, C, Qb Zs1=Zs2=Zs3 Yes No Zs1'=Zs2'=1/3*(Zs1+Zs2+Zs3) Update Zb t<tmax Yes No t=t+dt End Figure 3.3 Flow chart of the program 3.4 Case Study 3.4.1 Case 1: Steady Flow in Flume with Vegetation The developed model is applied to simulate a laboratory experiment in an open channel experimental flume (Baptist, 2005). The experimental flume is 35 m long and 80 cm wide; it is a straight, horizontal open channel with a concrete bottom and glass walls (Figure 3.4). A longitudinal section of artificial, flexible vegetation with a density of 400 m-2 was installed over a length of 15.85 m. The length of plants was 27 cm. Vegetation 54 stems were mounted onto 18mm wood-cement boards by sticking the plant into 2.0 mm diameter drilled holes. The alignment of vegetation is rectangular with a spacing of 5 by 5 cm. A 9-cm thick layer of sand was distributed evenly between the submerged plants. The quartz sand has a D50 of 321 μm and a D90 of 450 μm. Three runs were carried out with plants mounted to the flume floor, and another three on bare sediment. Detailed bed elevation profiles were measured in Run 2 and 3, which were selected to test the model performance. Flow discharges for Run 2 and 3 were 0.129 m3/s and 0.106 m3/s, respectively; and the durations of Run 2 and 3 were 30 hours and 32 hours. The experimental vegetation is artificial plants with 2mm thick stems and leaves; each leaf was 15mm long and 4mm wide at its widest point; and the leaves were placed along the stem in alternating groups with 5 leaves for each group. The vegetation coverage was calculated as 12% from the plant size and density. Since the leaves were not rigid, the vegetation coverage of 12% was overestimated. It turned out that 10% yielded better results than using 12%. Therefore, the vegetation density in both runs is chosen as 10%. Since the channel bottom is impermeable concrete, the infiltration depth is set as zero. The non-equilibrium recovery coefficient is calculated by using Eq. (3.3) and Table 3.1 shows the recovery coefficient ranges from 5.33 to 6.15. The adaptation length is set as 1.52m, which is approximately 5 times of the flow depth. There are 30 nodes in the domain, the grid spacing ranges from 0.2 to 0.82 m, and the simulation time step is 0.02 s. 55 Figure 3.4 Flume set-up and vegetation arrangement for the experiment of Baptist(2005) Table 3.1 Parameters used in the cases Symbol Parameter Case 1 Case 2 Δt Time space (s) 0.02 0.03 Δx Cross section interval (m) 0.2~0.82 91.4-182.9 λ Vegetation density 10% 15% hv Vegetation height (m) 0.27 1.52 d50 Sediment size (mm) 0.321 see table 2 d90 Sediment size (mm) 0.45 see table 2 L Adaptation length 1.64 121.9 α Recovery coefficient (from Eq.(8)) 5.33-6.15 3.2-20.2 Ks Saturated hydraulic conductivity(cm/hr) 1.09 Hf Capillary pressure head at the wetting front(cm) 11.01 Md Soil moisture deficit 0.29 Figures 3.5 and 3.6 are the simulated and measured bed profiles starting at x= 2m for Run 2 in the vegetation zone along the channel at t=13 and t=30 hours. Bed surface 56 from x=0 to 2 m is erodible, but was not shown because no measurement was made for this reach. Almost all cross sections are eroded as shown in both figures. Bed forms were present although not discussed in Baptist (2008). According to Van Rijn (1984c), the type of bed form is ripple, approximately 7 cm high as shown in Table 3.2. The erosion reached 4 cm at the last cross section when the experiment had run for 30 hours. More erosion can be seen downstream of the vegetation zone because flow condition changes rapidly from the vegetation to the bare sediment zone. The calculated results matches well with the measured at t=13 hours in Figure 3.5. At t=30 hours (Figure 3.5), bed erosion increases comparing to that at t=13 hours. A sand dune was formed at the beginning of the vegetation section due to local scour (Baptist 2005), which is not captured by the simulation. This attributes to the limitation of one dimensional model’s Bed level(m) capability of simulating local scour induced by the flow turbulence. 0.05 0.04 0.03 0.02 0.01 0.00 measured at t=0 h -0.01 measured at t= 13 h -0.02 calculated at t=13 h -0.03 2 4 6 8 10 12 14 x(m) 16 Figure 3.5 Measured (t = 0h and t =13h) and calculated (t = 13h) bed levels for Run 2 Bed level(m) 57 0.05 0.04 0.03 0.02 0.01 0.00 measured at t=0 h -0.01 calculated at t=30 h -0.02 measured at t= 30 h -0.03 2 4 6 8 10 12 x(m) 16 14 Figure 3.6 Measured (t = 0h and t =30h) and calculated (t = 30h) bed levels for Run 2 Table 3.2 Results related to bed form for Case 1 Test 2 Test 3 Measured (t=30hrs) Calculated (t=30hrs) Measured (t=32hrs) Calculated (t=32hrs) d* T Δ(m) Bed form type 0.31 8.12 _ _ _ 0.489 0.291 8.12 2.21~2.93 0.07~0.073 Ripples 0.287 0.46 0.27 8.12 _ _ 0.29 0.454 0.268 8.12 1.44~2.27 0.053~0.062 At x =10 m Q (m3/s) h (m) u (m/s) Fr 0.129 0.305 0.53 0.129 0.329 0.106 0.106 Ripples d* = dimensionless particle diameter; T = transport parameter, Δ = height of dunes Figure 3.7 and 3.8 show the results for Run 3 at t=14.5 hours and t= 32 hours. Based on flow and sediment data, bed form is ripple with an approximate height of 5.3~6.2cm according to Van Rijn (1984c)’s Diagram. The calculated bed surface profiles fit well with the measured. The erosion pattern is similar to Run 2 although less erosion was observed in Run 3 because the discharge for this run is much smaller. 58 Bed level (m) 0.05 0.04 0.03 0.02 0.01 measured at t=0 h 0.00 measured at t=14.5 h -0.01 calculated at t=14.5 h -0.02 -0.03 2 4 6 8 10 12 14 x(m) 16 Bed level (m) Figure 3.7 Measured (t = 0h and t =14.5h) and calculated (t = 14.5h) bed levels for Run 3 0.05 0.04 0.03 0.02 0.01 0.00 measured at t=0 h -0.01 measured at t=32 -0.02 calculated at t=32 -0.03 2 4 6 8 10 12 14 x(m) 16 Figure 3.8 Measured (t = 0h and t =32h) and calculated (t = 32h) bed levels for Run 3 3.4.2 Case 2: 2006 Flash Flood in Santa Cruz River, Tucson, AZ 3.4.2.1 Study Area The Santa Cruz River is an ephemeral river passing through the City of Tucson in Arizona. The Santa Cruz River has two major tributaries, Rillito River and Canyon Del Oro (CDO) River. Two USGS stream gauges, Tucson and Cortaro, are available on the 59 Santa Cruz River, while one (Ina Gauge) on the CDO River, and two (Dodge and Lo Cholla Gauge) on the Rillito River (See Figure 3.9). The simulation reach from Tucson Gauge to Cortaro Gauge on the Santa Cruz River is 20.92 km, including two tributaries: 15.77 km of Rillito River and 3.22 km of CDO River. The topographic data are a 1.52 1.52 m DEM obtained from airborne LIDAR survey in 2005. This DEM was used to cut cross sections along the rivers as geometric input data. There are 134 cross sections for the Rillito River, 163 for the Santa Cruz River, and 25 for the CDO River. The distance range between two cross sections is 91.44-182.88 m. Each cross section has about 80-200 surveyed elevation data. The upstream boundary conditions are stage hydrographs at the Tucson Gauge on the Santa Cruz River, the Dodge Gauge on the Rillito River, and the Ina Gauge on CDO River. 60 Cortaro CDO Ina La Cholla Santa Cruz Dodge Rillito 0 2 4 mi Tucson Figure 3.9 Simulation area and USGS gauge location. Red dot (rectangular): simulation boundary. Blue dot (ellipse): gauge location 3.4.2.2 Flow, Sediment and Vegetation Data The storm duration is 96 hours from July 29th, 2006 to August 1st. During this event, considerable amounts of sediment were deposited in the river and many vegetation were uprooted and removed. The maximum flow rate reached 1073.21 m3/s at the Dodge Gauge in the Rillito River exceeding the 100-year discharge. Observed flow hydrographs in Tucson Gauge, Dodge Gauge, and Ina Gauge are shown in Figure 3.10. flow rate(m3/s) 61 1200 1000 Dodge gage, Rillito River Tucson gage, Santa Cruz River 800 Ina gage, CDO River 600 400 200 0 0 10 20 30 40 50 time(hrs) 60 70 80 90 100 Figure 3.10 Flow hydrograph in different gauges Surface material was sampled at several locations on the Santa Cruz River and Rillito River. These samples were dried and weighted at the soil laboratory at Civil Engineering Department at the University of Arizona. The d50 and d90 of surface material samples are tabulated in Table 3.3. According to sediment size and flow conditions, Van Rijn’s relations were used for calculating the equilibrium bed load transport rate because Van Rijn’s relations are valid for 0.09mm < d50 < 1.5mm, flow depth within 0.1-17 m, and flow velocity from 0.36-2.4 m/s (Van Rijn,1984a,b). Since no sediment inflow data is available, the sediment boundary conditions were set to be equilibrium load calculated by van Rijn’s (1984a, b) formula for both suspended load and bed load. The suspended load recovery coefficient was estimated by using equation (3.3) and ranged from 3.2 to 20.2; the bed load adaptation length was 121.9 m, which is approximately the distance between two cross sections based on Zhang and Duan’s (2011) work. 62 Table 3.3 d50 and d90 of sediment samples in different locations of Santa Cruz River and Rillito River Santa Cruz River Rauthrauff Cortaro Sanders Sunset Tangerine Ina Twin peak Avra Vally Trico d50 (mm) 1.50 1.50 1.09 0.42 1.85 1.70 0.47 1.45 0.96 d90 (mm) 25.40 27.20 16.00 0.67 7.51 12.70 25.70 3.82 2.86 Rillito River Dodge Country club Campbell Mountain First Stone Oracle La Canada La Cholla I-10 d50 (mm) 1.66 2.29 1.72 0.73 1.96 1.07 1.34 0.62 1.46 0.81 d90 (mm) 8.77 13.54 4.46 1.94 7.89 5.67 8.52 1.94 4.47 4.48 Vegetation on Santa Cruz River floodplain is mostly herbaceous(Stromberg and Tellman, 2009). The average height is 1.52 m, and the coverage percentage is about 15%. Since there has not been a large flood for several years prior to this event, vegetation has very well established in the main channel and floodplains. To evaluate whether vegetation impact is essential to sediment transport, two scenarios were selected: one assumes vegetation impacts is negligible, and the other accounts for the effect of vegetation. Time step was set as 0.03 seconds for both scenarios. It took about 3 hours to run each scenario. 3.4.2.3 Simulation Results The simulated results of flow discharge and bed elevation change in the Santa Cruz and Rillito Rivers are compared with the measurements. There is no measurement in the CDO River for comparison. Figure 3.11 and 3.12 showed the simulated flow discharges at the La Cholla and the Cortaro Gauges. Results from both scenarios matched measurements well for both high and low flows. At the La Cholla Gauge, the simulated discharge is 93.73 m3/s less than the 1st observed peak flow. This may attribute 63 to the flow from one tributary about 2.3 miles upstream of the gauge. No flow data is available from this channel. Other peak flows match well with the measured data. At the Cortaro Gauge, the maximum flow reaches 1158.16 m3/s. Both simulated results slightly over-estimated flow discharge at the receding limb although the differences are small. Figure 3.12 shows that the simulated results accounting for the vegetation effects are slightly better in the Santa Cruz River. The Nash-Sutcliffe efficiency factor is a common parameter to quantify the accuracy of hydrologic models. The mathematical definition is written as: n 2 (Oi Ci ) Nash - Sutcliffe efficiency 1 i n1 2 (Oi O) (3.23) i 1 where Oi and Ci are the ith observed and calculated data, respectively, and n is the total number of observed or calculated data. The Nash-Sutcliffe efficiency ranges from -∞ to 1. An efficiency of 1 corresponds to a perfect match of modeling results to the observed data. An efficiency of 0 indicates that the model predictions are as accurate as the mean of the observed data, whereas a less than zero efficiency occurs when the observed mean is a better predictor than the model. The closer the model efficiency is to 1, the more accurate the model is (Nash and Sutcliffe, 1970). The Nash-Sutcliffe efficiencies of flow discharges for all the simulations are between 0.8 and 1 as shown in Table 3.4, which indicates the simulated flow discharge is accurate. Since the Nash-Sutcliffe efficiencies are similar for scenarios with and without vegetation, this indicates the vegetation induced resistance is insignificant comparing to other resistance in simulating this large flood event. 64 flow rate(m3/s) 1400 1200 measured data not considering vegetation effect 1000 considering vegetation effect 800 600 400 200 0 0 10 20 30 40 50 time(hrs) 60 70 80 90 100 Figure 3.11 Simulation and measured flow rate result at La Cholla, Rillito River 1400 measured data 1200 not considering vegetation effects considering vegetation effects flow rate(m3/s) 1000 800 600 400 200 0 0 10 20 30 40 50 time(hrs) 60 70 80 90 100 Figure 3.12 Simulation and measured flow rate result at Cortaro gauge, Santa Cruz River 65 As to bed elevation changes, Figure 3.13 and Figure 3.14 showed the simulated bed elevation changes along the Rillito and the Santa Cruz River. The results without considering the vegetation impacts deviate significantly from the measurements. Considering the impact of vegetation, the results have been improved significantly; especially for the maximum bed elevation change. The changes of bed elevation are smaller at both the Rillito and the Santa Cruz River comparing to the results without vegetation effect, because vegetation decreases shear stress at bed surface so that sediment transport rate is reduced. From Table 3.5 we can see that the Root Mean Square Error (RMSE) of modeling error decreases after incorporating vegetation effect. Although the vegetation model doesn’t considerably affect flow hydrograph, it bed elevation change(m) significantly alters sediment transport regime and consequently bed elevation changes. 4.0 2.0 0.0 -2.0 measured data not considering vegetation effect considering vegetation effect -4.0 0 2000 4000 6000 8000 10000 distance from upstream(m) 12000 Figure 3.13 Bed elevation change along Rillito River 14000 16000 66 bed elevation change(m) 8 measured data 6 not cosidering vegetation effect considering vegetation effect 4 2 0 -2 0 5000 10000 distance from upstream(m) 15000 20000 Figure 3.14 Bed elevation change along Santa Cruz River Table 3.4 Errors analysis of flow hydrograph and bed elevation change Flow discharge NASH RMSE(ft) Santa Cruz River Rillito River Ignore Consider Ignore Consider vegetation vegetation vegetation vegetation 0.8863 0.8819 0.9591 0.9697 Bed elevation change Santa Cruz River Rillito River Ignore Consider Ignore Consider vegetation vegetation vegetation vegetation 1.8542 1.1147 1.9484 1.0206 3.5. Discussion Flow hydraulics and sediment transport in vegetated channel network are simulated using a non-equilibrium sediment transport model with consideration of vegetation induced drag force. The significance of introducing vegetation impacts are 67 illustrated in Section 3.4 (Figures 3.13 and 3.14). Other issues regarding how vegetation coverage influences the modeling results and non-equilibrium vs equilibrium sediment transport model are discussed in the following. 3.5.1 Influence of Vegetation Coverage Figure 3.15 and 3.16 showed a sensitivity analysis of bed elevation change in the Rillito River and Santa Cruz River if changing vegetation coverage to 10%, 15%, and 30%, respectively. The results in Figure 3.15 and Figure 3.16 showed that smaller vegetation coverage resulted in more erosion and sedimentation. At larger vegetation coverage, bed elevation change becomes smaller. This result confirms that vegetation increases flow resistance and decreases flow velocity and bed shear stress in vegetated area, so high density vegetation coverage result in less erosion. elevation change(m) 3.0 measured data λ=0.1 2.0 λ=0.15 λ=0.3 1.0 0.0 -1.0 -2.0 -3.0 0 2000 4000 6000 8000 10000 distance from upstream(m) 12000 14000 16000 Figure 3.15 Sensitivity analysis of bed elevation change along Rillito River on vegetation density bed elevation change(m) 68 6.0 measured data λ=0.10 λ=0.15 4.0 λ=0.3 2.0 0.0 -2.0 0 5000 10000 distance from upstream(m) 15000 20000 Figure 3.16 Sensitivity analysis of bed elevation change along Santa Cruz River on vegetation density 3.5.2 Significance of Non-Equilibrium Model In our non-equilibrium sediment transport model, the bed elevation change was calculated by solving the Exner equation for bed surface layer as expressed in Eq.(2.5). Eq.(2.5) can be discretized with the explicit scheme adopted in this study as: zb n 1 zb n t 1 Bs (Cain Ca*in ) Qbi n Qb*i n B 1 pm L (3.24) where zb = bed elevation. In equilibrium sediment transport models, the geomorphic change of the stream bed can be calculated by solving the sediment continuity equation (Exner equation) given by (pp. 426, Sturm 2001): B1 p m z b Qt 0 t x (3.25) 69 where Qt = total sediment load including bed load and suspended load. It is assumed that the sediment transport rate is equal to the sediment transport capacity everywhere in the channel, i.e., Qt Qt* (3.26) Therefore, the bed deformation rate is calculated as: z b Qt* 1 t B1 p m x (3.27) Eq. (3.25) can be discretized with the explicit scheme adopted in this study: zbin 1 zbin t 1 Qt*i n Qt*i 1n x B 1 pm (3.28) When comparing Eq. (3.24) and Eq. (3.28), it can be easily seen that the bed elevation calculated by the equilibrium model is a function of the grid size, and therefore is grid-dependent, an undesirable property of a model. We incorporate the equilibrium model into our numerical model and simulate the Run 2 in Baptist (2008), by using 7 nodes and 10 nodes in the domain. To simplify the process, suspended load is neglected. The measured and simulated bed profiles at the end of the simulation (t = 30 hours) are plotted in Figure 3.17. The measured and simulated profiles from the non-equilibrium model are also plotted for comparison. Results from non-equilibrium model are better in both figures. When comparing the results by using 7 nodes and 10 nodes, it is clear that the number of nodes used in the equilibrium simulation significantly affected the simulated bed elevation change. However, the simulated bed profiles did not show much difference when applying non-equilibrium model. In the equilibrium model test, when the number of grid cells is set larger than 10, the solution becomes unstable. As the grid 70 becomes finer, the bed elevation change in one time step becomes larger. The fast changing bed elevation produces an unrealistic, but significant bed surface gradient term Bed level(m) in the momentum equation and causes the instability of flow solutions. 0.04 0.02 0.00 measured at t=0 h -0.02 measured at t= 30 h eq.model, 10 nodes non-eq. model, 10 nodes -0.04 eq. model, 7 nodes non-eq. model, 7 nodes -0.06 2 4 6 8 10 12 14 x(m) 16 Figure 3.17 Comparison of results from non-equilibrium and equilibrium model using 7 nodes and 10 nodes at t = 30 hours, respectively 3.6 Conclusions A one-dimensional flow and sediment transport model for vegetated channel network was developed. Both submerged and non-submerged vegetation were considered in the model to account for the vegetation influence. Vegetation induced roughness coefficient was used in the momentum equation; grain resistance is separated from the sidewall, vegetation, and bed form resistance to calculate sediment transport rate. The grain resistance is a function of vegetation density, and therefore the dense the 71 vegetation, the less erosion. The sediment transport model solved both bed load and suspended load transport equation. The non-equilibrium sediment transport algorithm is adopted for bed elevation changes. The model has been tested by simulating two cases: one is a steady flow experiment in a vegetated channel, and the other is a large flash flood event in the Santa Cruz and Rillito River basin. The simulated results were compared with the observed data. In the experimental case, bed profiles from simulated results agreed well with the experimental results, although the dune occurred in Run 3 cannot be simulated because this 1D model cannot capture flow turbulence. When simulating 2006 flash food in the Santa Cruz and Rillito river network, the simulated flow hydrograph and bed profiles showed reasonable agreements with measured data. We also found the model accounting for the impacts of vegetation gave better results of flow and sediment transport, especially bed elevation changes. The influence of vegetation on sediment transport and channel mrophodynamics has been successfully simulated by the model. 72 CHAPTER 4 APPLICATION OF TWO-DIMENSIONAL SURFACE ROUTING MODEL FOR SANTA CRUZ WATERSHED BY CONSIDERING VEGETATION COVERAGE INLUENCE 4.1 Introduction Surface flow routing, including overland and channel flow routing, refers to the process that a precipitation generated surface runoff moves over land surface from source areas to an outlet (Figure 1.1). The simulation of surface flow routing over a watershed are accomplished by using either two models for overland and channel flow (Julien, et al., 1995; Qu and Duffy, 2007), separately, or one model to simulate both overland and channel flow (Cea, et al., 2010; Kim, et al., 2012; ). The disadvantage of the first kind of model is the difficulties of data processing, and the second method is commonly adopted. Nearly all the rainfall-runoff models for predicting surface flows are simply based on the solutions of kinematic wave equations (Vivoni et al., 2007; Yang et al., 1998) or diffusion wave equations (Qu and Duffy, 2007). An advanced 2-D hydrodynamic and sediment model, CHRE2D, has been developed in our research group by Yu and Duan (2013), Yu and Duan (2014). CHRE2D solved the surface flow by fully two-dimensional shallow water equations. In order to increase the stability of the model, the KWA was used for thin water depth in CHRE2D. In this study, to improve the capability of CHRE2D to account for vegetation impacts, friction terms in the momentum equations are modified by addressing the 73 vegetation coverage. The improved CHRE2D model was verified by an observed storm event. 4.2 Modifications to CHRE2D Model 4.2.1 Quantification of Vegetation Coverage 70 Satellite photos were used to analyze vegetation coverage, the satellite photo coverage area are shown in Figure 4.1. Each photo was portioned into 6 layers; the vegetation layer was extracted and used to calculate vegetation coverage. The extracted vegetation layers for representative photos are shown in Figure 4.2. And the vegetation coverage for different locations are listed in Table 4.1. 4.2.2 Incorporation of Vegetation Influence The modified roughness coefficient is calculated by equations derived by Cheng (2011) as introduced in Chapter 3. For the Santa Cruz River Watershed, the vegetation are emerged for the most of time, then the representative Chezy coefficient is presented as CR g (1 )3 d 2CD h (4.1) where = vegetation density; h = flow depth; CD = drag coefficient in Eq.3.9. The Manning’s coefficient in Eq. (momentum) was calculated as n h1/6 / CR . The updated 74 roughness coefficient taking account of the vegetation density was imbedded into the CHRE2D model to modify Eq.2.9. Figure 4.1 Satellite photos coverage area 75 Figure 4.2 Extracted vegetation layers for representative photos Table 4.1 Vegetation coverage for different locations Site NO. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 Coverage % 4.168 16.231 6.441 21.914 12.235 11.491 14.047 8.668 20.541 17.693 15.825 2.051 33.465 18.792 17.574 10.336 18.428 5.6564 Site NO. 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 Coverage % 16.671 18.952 16.337 11.483 9.1662 18.542 11.801 9.7738 17.471 12.847 15.975 13.85 10.602 15.736 13.036 11.199 10.193 15.78 Site NO. 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 Coverage % 11.099 3.8193 13.136 14.227 7.7058 13.069 9.2967 12.036 17.643 2.9747 13.664 17.852 8.9102 17.575 12.415 17.807 4.5685 12.138 Site NO. 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 Coverage % 11.095 16.259 11.977 9.4191 10.838 24.765 4.2486 18.971 15.785 11.33 19.603 20.269 21.254 12.931 8.2697 16.05 76 4.2.3 Other Hydrological Processes Other hydrological processes including precipitation, interception and infiltration used in CHRE2D are summarized here. The precipitation intensity is interpolated by the inverse distance squared approximations: NRG im ( jrg , krg ) d2 i ( j , k ) m 1 NRG m 1 2 m 1 d m (4.2) where i( j, k ) is the rainfall intensity in cell ( j, k ) ; im ( jrg , krg ) is the measured rainfall intensity by the mth rainfall gauge at cell ( jrg , krg ) ; d m is the distance from cell (i, j ) to mth rainfall gauge at cell ( jrg , krg ) ; NRG is the total number of rainfall gauges. The interception loss is modeled by the concept of interception depth. When the intercepted water does not reach land surface, the rainfall excess rate is equal to zero in each time step. As soon as the interception depth is satisfied, the rainfall excess is generated and accounted in mass conservation equation. The Green-Ampt model is used for calculating the infiltration loss. By neglecting the ponding on the surface, the GreenAmpt model can be written as: H f Md f K s 1 F (4.3) where f is the infiltration rate; K s is the saturated hydraulic conductivity; H f is the capillary pressure head at the wetting front; M d is the soil moisture deficit; F is the total 77 infiltrated depth. At each time step, the infiltrated loss is subtracted from the interpolated rainfall intensity. The resultant rainfall excess is adopted in Eq. (2,9) as the source term. 4.3 Study Site and Data Source 4.3.1 The Study Site The Santa Cruz River Watershed (SCRW), located in the south central part of the Arizona (Figure 4.3), is a trans-boundary watershed with an elevation ranges from 2192 to 9337 feet. The Santa Cruz River (SCR) is an ephemeral tributary that drains into the Gila River, a tributary to the Colorado River (Shamir et al., 2007). The Santa Cruz River flows to the South and makes a 25-mile loop through Mexico before re-entering the United States 5 miles of Nogales, Arizona. Afterwards, the river flows northward to its confluence with the Gila River. The study area for the current work is the watershed encompassing the reach of the Santa Cruz River within the US, which is approximately 8,000 square miles, representing about 10% area of the State of Arizona. The resolution of digital elevation model (DEM) used in this study is 100 m extracted from the Lidar survey in 2005 by the Pima County Flood Control District. 78 Figure 4.3 Map of the Santa Cruz River Watershed (Norman et al., 2010) 4.3.3 Precipitation Data Source A 24 hours rainfall event of July 15th, 1999 was selected to calibrate the rainfallrunoff model. The hourly gridded precipitation data which has a resolution of 32 km is obtained from NLDAS (http://ldas.gsfc.nasa.gov/nldas/NLDAS2forcing.php). rainfall distribution at t=5hr, t=11hr and t=21hr were shown in Figure 4.4. The 79 Figure 4.4 Rainfall depth (mm) distribution at different time (t = 5, 11, 21 hours) for July 15th, 1999 flood event. 4.4 Model Application and Calibration The CHRE2D model has already been verified by many experimental and field cases (Yu and Duan, 2013; Yu and Duan, in press). However, the modeling parameters, such as infiltration rate, need to be calibrated for different cases. A 24 hours rainfall event of July 15th, 1999 was selected to calibrate the rainfall-runoff model. The observed flow discharges at the Cortaro gauge, located near the downstream outlet of the study reach, were used to compare with calculated results. The maximum flow rate of this event was 13,700 cfs at Cortaro Gauge, which was the largest flood in 1999. The observed flow hydrograph of Cortaro gauge was used for model calibration. The soil type of SCRW is gravel sandy loam, the saturated hydraulic conductivity (Ks) is set as 1.09 cm/hr, and the calibrated value is 1.5cm/hr. The capillary pressure head at the wetting front Hf is set as 11.01cm, and the calibrated one is 12cm. The soil moisture deficit Md is 0.29 in the model 80 (Rawls et al., 1983). The interception loss is calibrated as 0.5mm. The Manning’s roughness coefficient is 0.03. The grid size is 100 m by 100 m. The time step for the simulation ranges from 1.0 s to 10 s; it takes about 1.5 hours to run a 24-hour storm event. The model runs on a 12-core server. The measured and simulated hydrograph at the Cortaro gauge were shown in Figure 4.5. The simulated hydrograph matched the peak arriving times and the peak discharges well. Though the measured low flow at the first several hours was not captured by the model, the results from the watershed model accurately estimated flood peak discharge, which is essential for flood magnitude and frequency analysis. Flow depth at different times, t=6hr, t=12hr, and t=22hr, were shown in Figure 4.6. The calibrated model is used to simulate surface flow routing for the historical and future periods in next chapter. 16000 Measured 14000 Simulated Flow rate(cfs) 12000 10000 8000 6000 4000 2000 0 0 5 10 Time (hrs) 15 20 25 Figure 4.5 Measured and simulated hydrograph for Cortaro gage of July 15th, 1999 81 Figure 4.6 Water depth (m) at different time (t = 6, 12, 22 hours) for July 15th, 1999 flood event 4.5 Conclusions A two-dimensional surface flow routing model, CHRE2D, was modified by considering the vegetation influence on Manning’s roughness factor. Then, the improved model requires the calculation of the Manning’s roughness coefficient based on the vegetation coverage. The watershed model is then calibrated by simulating an observed flood event in the SCRW. The calibrated model is used for further simulations of projected surface runoff event in the next Chapter. 82 CHAPTER 5 IMPACTS OF CLIMATE CHANGE ON MAGNITUDE AND FREQUENCY OF FLOOD IN LOWER SANTA CRUZ RIVER 5.1. Introduction Flood magnitude and frequency play an important role in the design of hydraulic structures. It is well known that the climate change will result in the change of flood magnitude and/or frequency. The frequent occurrences of extreme floods in recent decades have received much interest. For example, the Mississippi River Flood in 2010, and the nearly 500 year flood occurred in the Rillito River, AZ in 2006. Many researches attributed those abnormalities to climate change due to carbon emissions. Studies of climate change concluded a global surface temperature warming for the next century (Griggs and Noguer, 2002; Klein Tank et al., 2002; Parker et al., 1992). It is expected that the warming climate will lead to increase in the magnitude of extreme precipitation (Arnbjerg-Nielsen, 2006; Hennessy et al., 1997; Schmidli and Frei, 2005; Zhai et al., 2005) and other climate properties (e.g., snow melt) contributing to flooding across the globe. A number of studies have re-calibrated the flood magnitude and frequency curves by incorporating the impact of climate change. Most of those studies used a simplified rainfall-runoff model to route precipitations predicted from the climate model (e.g. RCM) at a given watershed. Kay et al. (2006b) used the simulated data from RCM to identify possible flood frequency changes by using a conceptual rainfall-runoff model between 1970s and 2080s for 15 catchments across the Great Britain. His results showed that the 83 annual averaged rainfall decreased for all the catchments except for one, and the flood magnitudes for most return periods are increased. Li et al. (2013) applied two conceptual rainfall-runoff models to simulate runoff using the historical and projected future precipitation in Tibet. They found the mean annual runoff increased 13%, and the average temperature increased 1oC in the study area. Similar researches (Booij, 2005; Chen and Grasby, 2014; Hay et al., 2002; Leonard et al., 2008; Mailhot et al., 2007; Mirza et al., 2003; Raff et al., 2009) for different regions all over the world showed that the change of flood magnitude and frequency varied regionally depending on the location and elevation because of the complex watershed characteristics. In this dissertation, flood magnitude and frequency curve will be developed using both historical and climate model projected daily and annual flow data. A physical based two dimensional hydrodynamic rainfall-runoff model (Yu and Duan 2012; Yu and Duan 2014) is used to route the hourly precipitation data for the historical (1990-2000) and future periods (2031-2040, 2071-2079) for the Santa Cruz River Watershed in Tucson, AZ. The precipitation output from the global climate models (GCMs) has commonly been used to investigate the impact of climate change on flood risk (Cameron et al., 1999; Merritt et al., 2006). GCMs typically have a resolution of approximately 200-400 km which is too coarse for hydrological model (Bell et al., 2007). Because of the coarse spatial resolution of GCMs and the uncertainty of their precipitation output at a fine temporal resolution, the results from GCMs are not suitable for direct flood modelling (Kay et al., 2006b). The high resolution RCM embedded within a GCM can provide a suitable scale for reliable use to assess the impact of climate change on stream flow. 84 Therefore, the hourly precipitations from RCM model were used in this study. The hourly precipitations were bias corrected and then used as input to a rainfall-runoff model to simulate flood flows in rivers. Flood frequency curve is required for designing in-stream engineering structures, such as bridges. One of the key assumptions of flood frequency analysis is that the return period of a flood peak of given magnitude is stationary with time. This assumption has always been questioned, and appeared to become even more questionable in the future because of climate change. The analysis that solely relies on historical records can no longer be suitable for making reliable inferences on the future behavior of the hydroclimate conditions. Nowadays, the flood flows generated from projected climate data together with historical records are widely used for flood risk analysis. Nearly all the rainfall-runoff models for predicting flood flows are based on the solutions of kinematic wave (Vivoni et al., 2007; Yang et al., 1998) or diffusion wave (Qu and Duffy, 2007) approximations. Although the conceptual model is usually computationally efficient and easy to handle, the disadvantage is the accuracies and inability to route surface flow over complex terrains. The common input precipitation data for conceptual models are daily or monthly averaged precipitation, which resulted in the daily or monthly averaged flow in the river. However, water related hydraulic structures require the peak discharge as the design flow, such as 100-year flood flow for bridge design. The daily averaged flow can be much less that the peak flow for the Southwest US because of the short duration and high intensity precipitation event. Hanel 85 and Buishand (2010) found the increase in large quantiles of the daily maxima was much smaller than that in the quantiles of the hourly maxima at the end of the 21st century. Therefore, the two-dimensional physical based hydrodynamic watershed model, CHRE2D, developed by Yu and Duan (2013) was used in this paper to route surface flow over the Santa Cuz River watershed to evaluate the potential changing of flood intensity and frequency. The objective of this chapter is to analyze the possible flood magnitude and frequency change caused by climate change in the Santa Cruz River Watershed. Instead of historical records, the precipitation data generated from the WRF (Weather Research and Forecasting) Regional Climate Model was routed through the watershed using CHRE2D watershed model. Three periods were simulated: the historical period of 19902000, the future periods of 2031-2040 and 2071-2079. In particular, we applied quantilebased mapping bias correction method to all three periods, calibrated the CHRE2D model using the rainfall event of July 15th, 1999, compared the simulated stream flow for the historical (1990-2000) period with observations, and developed new flood magnitude and frequency curves based on climate projected precipitations. 5.2 Watershed Description and Data Source 5.2.1 The Study Site For the SCRW, the mean monthly precipitation in the summer is greater than that in the winter (Wood et al., 1999). The summer rainy season starts from July to September, 86 while the winter rainy season is from December to March. The spring and fall months in Arizona usually are dry season, and winter and summer seasons are the only sources of precipitation in the study area. The mean annual precipitation at the Nogales gauge from 1914 to 2000 was 422 mm, consisting of an average 59% in the summer and 29% in the winter (Shamir et al., 2007). 5.2.2 Climate Data Source The climate data for the study area was extracted from the output of Weather Research and Forecasting (WRF) regional climate model (Dominguez et al., 2012). The regional climate model WRF driven by the HadCM3 GCM was executed continuously for 111 years (1967-2079) with a spatial resolution of 35 km and a temporal resolution of 6 hours. Due to the limitation of currently computation power, it is unrealistic to run the 111-year continuous simulation at a high resolution. Three periods were selected to represent the typical current and future climate. Current climate conditions are represented by the time period of 1990-2000; changed climate conditions are represented by the time period of 2031-2040 and 2071-2079. A further downscaled simulation was performed to refine the precipitation data at 10 km spatial resolution and hourly temporal resolution for the selected three periods. The gridded precipitation data downscaled from the WRF model was used as input into the hydrological model. 5.2.3 Bias Correction of Precipitation Data It is well known that, unless the output from the climate model is corrected for biases, the projected precipitations can be unrealistic and thus of limited use (Sharma et 87 al., 2007). Bias correction was traditionally used for correcting daily or monthly distributions (Fowler and Kilsby, 2007; Piani et al., 2010; Yang et al., 2005). Bias correction of precipitation data at hourly scale is needed to satisfy the input requirement for the hydrological model. A two-step quantile-based mapping method derived by Wood et al. (2002) was modified and applied to reduce the errors between the daily observed and the WRF simulated precipitations. Monthly precipitation outputs from the climate model within the study area were bias-corrected on a cell-by-cell basis. The downscaled WRF hourly precipitation data for 1990-2000 with a resolution of 10 km was aggregated to monthly precipitation and then re-gridded to 1/8 degree cell in the first step. The observed monthly precipitation was obtained from Maurer et al. (2002) on 1/8 degree grid for the same period. The simulated and observed monthly precipitation is assigned a non-exceedance percentile for a given month for the entire eleven year period. For example, there are eleven monthly precipitation data for January for the entire simulation period. The eleven monthly precipitation data are sorted in a descending order, and each is assigned a non-exceedence percentile. The same procedures are applied for the observed monthly precipitations in the same period. The bias correction are expressed as multiplicative anomalies as shown in Eq. (5.1). M ihist ,q Pi ,obs q Pi ,wrf q (5.1) 88 th wrf where Pi ,obs quantile of observed and simulated montly q and Pi , q represent the q precipitation from WRF model for the ith month during the period of 1990-2000, respectively; M ihist is the scaling factor, representing the qth quantile multiplicative ,q anomalies for the ith month for the current period. The bias-corrected monthly precipitations for the current period are calculated using Eq. (5.2). The scaling factor was then applied to the future two periods: 2031-2040 and 2071-2079 as shown in Eq. (5.3). The above procedure was repeated for each month from January to December. The bias correction was applied atr each cell for a total of 45 cells in the study area. hist Pi wrf Pi ,wrf q M i ,q (5.2) hist Pi fut Pi ,fut q M i ,q (5.3) th where Pi ,fut quantile of WRF simulated precipitation for the ith month in q represents the q the future period; Pi wrf and Pi wrf represent the bias-corrected precipitation for the ith month in the current and future period, respectively. Figure 5.1 shows the bias correction results for for a selected cell during three periods. For each cell, the bias-corrected monthly median precipitation is the same as in the observed data for period 1990-2000. It shows that the raw data from WRF model overestimated the precipitation, especially in the wet seasons. The ratios of observed monthly precipitation and the WRF simulated monthly precipitation were applied to future periods cell by cell, which reduced the bias of simulated precipitations of future periods. 89 Figure 5.2, 5.3 and 5.4 showed the bias-corrected and raw monthly precipitation data for each year of three periods, respectively. 100 observed 1990-2000 WRF B-C 1990-2000 WRF raw 1990-2000 WRF B-C 2031-2040 WRF raw 2031-2040 WRF B-C 2071-2079 WRF raw 2071-2079 90 80 Precipitation (mm) 70 60 50 40 30 20 10 0 1 2 3 4 5 6 7 8 calendar month 9 10 11 12 Figure 5.1 Monthly precipitation (P) raw data and bias-corrected data (B-C) for a selected cell (cell number marked as 33). Observed monthly median P for 1990-2000 and WRF model raw and B-C monthly median P data for different periods 90 200 B-C raw B-C median raw median 180 160 Precipitation (mm) 140 120 100 80 60 40 20 0 1 2 3 4 5 6 7 8 calendar month 9 10 11 12 Figure 5.2 WRF model raw and bias-corrected (B-C) monthly P and monthly median precipitation P data for 1990 -2000 for a selected cell (cell number marked as 33). 300 B-C raw B-C median raw median Precipitation (mm) 250 200 150 100 50 0 1 2 3 4 5 6 7 8 calendar month 9 10 11 12 Figure 5.3 WRF model raw and bias-corrected (B-C) monthly P and monthly median precipitation P data for 2031- 2040 for a selected cell (cell number marked as 33). 91 400 B-C raw B-C median raw median 350 Precipitation (mm) 300 250 200 150 100 50 0 1 2 3 4 5 6 7 8 calendar month 9 10 11 12 Figure 5.4 WRF model raw and bias-corrected (B-C) monthly P and monthly median precipitation P data for 2071-2079for a selected cell (cell number marked as 33). The spatial averaged monthly median precipitation data are presented in Figure 5.5. The observed spatial averaged monthly median precipitation does not exactly match with the spatial averaged WRF bias-corrected data in Figure 5.5 because the bias correction was applied individually for each cell. The monthly precipitation medians in two future periods are larger than that for the period 1990-2000. The WRF model overestimated the average precipitation in the summer season and slightly underestimated it in the winter season. 92 120 observed 1990-2000 WRF B-C 1990-2000 WRF raw 1990-2000 WRF B-C 2031-2040 WRF raw 2031-2040 WRF B-C 2071-2079 WRF raw 2071-2079 Precipitation (mm) 100 80 60 40 20 0 1 2 3 4 5 6 7 8 calendar month 9 10 11 12 Figure 5.5 Monthly median precipitation (P) raw data and bias-corrected data (B-C) for different periods with spatial average Followed by the bias correction step, an additional step was taken to disaggregate the monthly data into a daily time series. For each cell, the daily precipitation values for a given year and month were scaled to match the monthly total precipitation for the same month. Figure 5.6 shows the disaggregate result of daily precipitation for a selected cell. The comparisons of the observed daily precipitation with the bias-corrected WRF modeling results and the WRF model’s raw results are shown in Figure 5.6 (a) and (b), respectively. It can be seen that the bias-corrected result matched well with the observation. The Root Mean Square Errors (RMSEs) between the biased corrected and the observed precipitations for each cell are summarized in Table 5.1. The calculated RMSE ranges from 4.21 to 6.92 (mm), the normalized root-mean-square deviation which indicate the residual variance ranges from 6.94% to 13.75% with most of cells less than 93 10%. Since no hourly observed precipitation data is available for period 1990-2000, we will not compare the hourly bias-corrected precipitation with observations. (a) 80 Observed daily P WRF B-C daily P Precipitation (mm) 70 60 50 40 30 20 10 0 500 1000 1500 (b) 2000 2500 Continus day number (days) 3000 3500 4000 80 Precipitation(mm) Observed daily P WRF raw daily P 60 40 20 0 500 1000 1500 2000 2500 Continus day number (days) 3000 3500 4000 Figure 5.6 Daily precipitation (P) data for a selected cell (cell number marked as 33) for period 1990-2000. (a) Comparison of observed daily P and WRF model bias-corrected daily P, (b) Comparison of observed daily P and WRF raw daily P. Table 5.1 Root-mean-square-error of WRF model bias-corrected daily precipitation and observed daily precipitation for all cells Cell # 1 2 3 4 5 6 7 8 9 RMSE(mm) Cell # RMSE(mm) Cell # RMSE(mm) Cell # RMSE(mm) Cell # RMSE(mm) 6.9235 10 6.4961 19 6.9113 28 4.4060 34 4.2334 6.6674 11 5.6143 20 6.1986 29 4.5335 35 4.4713 6.3720 12 5.0630 21 6.3358 30 4.8463 36 4.3497 5.8454 13 6.5137 22 5.2490 31 4.8276 37 4.3270 6.0385 14 6.7290 23 4.8468 32 4.3710 38 4.2133 6.7084 15 6.0207 24 5.4447 33 4.2668 39 4.5897 6.8397 16 5.6664 25 5.8356 34 4.4569 40 4.8166 5.8534 17 4.6299 26 4.8862 35 5.0865 41 6.2054 6.2025 18 5.1663 27 4.6287 36 5.2144 42 5.1340 94 20 WRF B-C hourly P WRF raw hourly P 18 16 Precipitation (mm) 14 12 10 8 6 4 2 0 500 1000 1500 2000 2500 3000 hour numbers 3500 4000 4500 5000 Figure 5.7 Hourly precipitation (P) raw data and bias-corrected data (B-C) for period 1990-2000 In this study, hourly precipitations are used as input data for hydrological model. A further step of disaggregating daily time series into hourly distribution is taken for each cell. The strategy is similar as disaggregating monthly data to daily data by scale daily precipitation to match the daily total precipitation. The hourly precipitation data of RCMWRF raw data and bias-corrected data for period 1990-2000 were shown in Figure 5.7. The bias-corrected hourly precipitation data are then interpolated back to a 10 km grid cells and used as the input for the hydrological model. 95 5.2.4 Watershed Model The impact of climate change on flood frequency is assessed using a physical based SWE-KWA watershed model, CHRE2D, developed by Yu and Duan (2013). The model has already been introduced and calibrated in Chapter 4. The model was successfully applied for Santa Cruz River Watershed, and the calibrated parameters were directly used in the simulations in this Chapter. 5.3 Results The CHRE2D model was used to simulate flow hydrograph for all three period. Because of the limitation on computational capability, it is not necessary to run each period continually. The summer and winter rainy seasons are the mainly source of precipitation for the SCRW, and during most days of Spring and Fall seasons, there is no precipitation. Therefore, only rainfall events in each period were simulated. Days without precipitation were deleted from the input precipitation data. In total, 96 rainfall events were simulated for the historical period of 1990-2000, 80 rainfall events for 2031-2040, and 70 rainfall events for 2071-2079. The Cortaro gauge has observed flows for the historical period 1990-2000, so the simulated results of flow discharge at the Cortaro gauge were used to verify the accuracy of simulated discharges. 5.3.1 Comparison of Observed and Simulated Results for Historical Period The accuracy of the calibrated watershed model was evaluated by comparing the simulated flow results at the Cortaro Gauge with the observations. Figure 5.8 compares 96 the observed and simulated percent of yearly peak flow exceeding a given discharge for the period of 1990-2000. The largest yearly peak discharge during this period is about 27,000 cfs for both simulated and observed data. The second largest simulated yearly peak during this period is about 9,000 cfs larger than observed data. The rest of simulated yearly peaks match well with the observed data. 60% of the yearly peak discharges are greater than 5,000 cfs for both the simulated and observed data. Statistics of annual observed and simulated peak discharges from 1990 to 2000 are shown in the first two rows in Table 5.2. The simulated mean annual peak flows is nearly the same as the observed one. Nevertheless, the standard deviation and skewness of annual peak flows are different. The weighted skewness and frequency factors are used to estimate flow rates of different return periods. As can be seen in the table, there is no obvious difference of skewness and frequency factors for observed and simulated data during this period. Figure 5.9 shows the current Log-Person III type flood frequency curves for the Santa Cruz River at Cortaro Gauge. The flood magnitude and frequency curves are estimated according to USGS 17B report. The solid line was calculated using the historical data from 1940 to 1998, 2001 to 2013, and the simulated data from 1999 to 2000. The dashed line was calculated using only the historical data from 1940 to 2013. The flood frequency curve calculated from the observed and simulated data matches well with the curve derived from only the observed data. For the 100-year return period flood, both curves predict the same flow discharge, which is 40,000 cfs. For the 200-year flow, there is 2,000 cfs difference between the results from two curves. 97 The percent of daily peak flows exceeding a given discharge for the observed and simulated 1990-2000 period was shown in Figure 5.10. Only 0.25% percent of daily peak discharges are larger than 5,000cfs for both observed and simulated data. There are 0.83% percent of daily peak flows greater than 1,000cfs for observed data and 0.76% percent for simulated data. Only four observed daily peak discharges are greater than 10,000cfs. For daily peak flows greater than 8,000cfs, the simulated data are over-estimated comparing with observed data. For flows less than 8,000cfs, the simulated data match with the observations. Daily peak flows are summarized in Table 5.3. Table 5.3 shows the frequency of daily peak flow greater than a given discharge for every year of each period. Results in this table show the frequency of daily peak flow exceeding a given discharge are similar for observed and simulated data during 1990-2000 period. The simulated results show the frequency of daily peak flow greater than 20,000 cfs is twice as much as that of observed data. One can see from results Figure 5.8 to Figure 5.10, most of the flood events during 1990-2000 are very small, only four events have discharges larger than 10,000 cfs. The watershed model results performed well for low to mid flows, but a bit overestimated the large floods. Flood magnitude and frequency curves obtained from observed and simulated data sets are similar with 2,000 cfs difference for the 200-year flow. 98 30000 25000 Discharge (cfs) 20000 15000 10000 Observed 1990-2000 yearly peak 5000 0 1 10 Percent of years exceeded (%) 100 Figure 5.8 Percent of yearly peak discharge exceeded certain discharge of observed and simulated data for 1990-2000 periods 50000 Discharge (cfs) 40000 30000 20000 10000 17B - Observed and simulated historical 17B - Observed hitorical 0 1 10 Return Period (years) 100 1000 Figure 5.9 Current Log-Person III Flood frequency curves for Santa Cruz River at Cortaro using USGS 17B (Solid line: using observed historical data from 1940-1998, 2001-2013 and simulated data from 1999-2000; dashed line: using observed historical data from 1940-2013) 99 30000 25000 Discharge (cfs) 20000 15000 10000 observed 1990-2000 5000 Simulated 1990-2000 0 0.01 0.1 1 Percent of days exceeded (%) 10 100 Figure 5.10 Percent of daily peak discharge exceeded certain discharge for observed and simulated 1990-2000 period 5.3.2 Flood Magnitude and Frequency Analysis Using Annual Maximum Data The percent of yearly peak discharges exceeding a given discharges for three periods are shown in Figure 5.11. Observed yearly peak flow rates for period 1990-2000 are used to represent historical condition. For historical period, 45% yearly peak flows exceeds 10,000cfs and 9% exceeds 20,000cfs. For period 2031-2040, 70% of yearly peak discharges are greater than 10,000cfs and 20% of yearly peak discharges are larger than 20,000cfs. The frequencies of floods exceed 10,000cfs and 20,000cfs for period 20312040 are twice as much as that for historical period. The curve for period 2031-2040 locates on the right of historical period curve, which indicates the magnitude and intensity of yearly peak discharges for future period 2031-2040 are increased compared with historical period. For period 2071-2079, there are also 70% of data greater than 100 10,000cfs and only 11% of data greater than 20,000cfs. When comparing data of period 2071-2079 with historical observed data, it is noticed that the magnitude and intensity of flood increased for all flow rate grades except for discharges between 10,000cfs and 15,000cfs. The statistical analysis results of above three periods can be found in Table 5.2. The mean yearly peak discharges for two future periods are greater than historical period, with the standard deviation smaller than historical period. Figure 5.12 shows the current and future Log- Person III flood frequency curves for Santa Cruz River at Cortaro Gauge. Current flood frequency curve was calculated using the historical observed data from 1940 to 2013. The future flood frequency curve was calculated using the historical data from 1940 to 2013 and the simulated data of 20312040 and 2071-2079. Comparing the current and future flood frequency curves, one can conclude the discharge of 100-year flood is increased by 3,000 cfs when including the climate generated flow data. It is about 7.5% of the current 100-year flood discharge The 200-year flood discharge is increased by 5,000 cfs, which is about 11.1% of the current 200-year flood discharge. The correlations of these two data sets are listed in Table 5.2. Although all the statistical parameters did not show a big difference between these two data sets, the Log-Person III flood frequency curves showed flood discharges for different return periods has been moderately increased when including the climate model generated future data. . 101 40000 35000 30000 Discharge (cfs) 25000 20000 15000 observed 19902000 10000 simulated 20312040 5000 0 1 10 Percent of years exceeded (%) 100 Figure 5.11 Percent of yearly peak discharge exceeded certain discharge for observed historical and simulated future periods 70000 60000 Discharge (cfs) 50000 40000 30000 17B - Future 20000 17B - Current Observed historical 10000 2031-2040 simulated 2071-2079 simulated 0 1 10 Return Period (years) 100 Figure 5.12 Current and future Log-Person III flood frequency curves for Santa Cruz River at Cortaro using USGS 17B (Solid line: current flood frequency curve using historical data from 1940-2013; dash line: future flood frequency curve using historical data from 1940-2013 and simulated data of 2031-2040 and 2071-2079) 102 Table 5.2 Statistical analysis results of yearly peak flow for different periods Xave Standard deviation of logarithms Sdev 3.732 Mean logarithm Observed period 19902000 Simulated period 19902000 Simulated period 20312040 simulated period 20712079 Observed historical period 1940-2013 observed historical 1940-1989, 2001-2013 and simulated 1990-2000 observed historical and all simulated Skewness Skewness of of logarithms logarithms Frequency factors for different recurrence interval years Cs Cw 2 10 50 100 0.520 -0.629 -0.302 0.050 1.245 1.889 2.102 2.292 3.664 0.682 -0.874 -0.387 0.064 1.233 1.841 2.039 2.213 3.946 0.463 -0.728 -0.327 0.054 1.241 1.875 2.084 2.269 3.993 0.325 -0.172 -0.126 0.021 1.267 1.986 2.233 2.457 3.891 0.358 -0.623 -0.475 0.079 1.220 1.791 1.974 2.131 3.880 0.403 -1.191 -0.747 0.124 1.175 1.636 1.772 1.884 3.908 0.365 -0.589 -0.471 0.078 1.220 1.793 1.976 2.135 5.3.3 Flood Frequency Analysis Using Daily Maximum Data In order to compare daily peak flow discharges of future periods and current periods, the percentages of daily peak discharge exceeding a certain discharge for three periods are shown in Figure 5.13. The observed daily peak flow discharges for period 200 103 1990-2000 are used to represent historical conditions. 0.25% of daily peak discharges are greater than 5,000 cfs for the period 1990-2000, 0.5% of data for the period, 2031-2040, and 0.65% of data for the period, 2071-2079. Comparing data for the period 1990-2000 with those for 2031-2040, the flood frequency curve moves to the right. This indicates that the flood magnitude and frequency increase from the historical to the future condition. The curve for period 2071-2080 also shifts to the right of period 1990-2000, which indicates the flood magnitude and frequency are larger than historical condition. Comparing two curves of future periods, the flood magnitude and frequency for period 2071-2079 is greater than 2031-2040 for flood discharge less than 12,000 cfs. The largest flood discharge is 36,851 cfs for period 2071-2079 and 28,756 cfs for period 2031-2040. The daily peak flow summary for these three different periods is listed in Table 5.3. Comparing the observed data for the period 1990-2000 with the simulated data for the period 2031-2040, there are 3.2 days with daily peak discharge greater than 1,500 cfs of every year during 2031-2040 and 2.36 days during 1990-2000. The frequency of daily peak discharge greater than 5,000 cfs during period 2031-2040 is twice as much as that for the period 1990-2000. When the daily peak discharge is greater than 20,000 cfs, the frequency during the period 2031-2040 is more than three times as much as that for the period 1990-2000. For both periods: 1990-2000 and 2071-2079, the frequencies for all discharge are greater than those in the period 1990-2000. For period 1990-2000 and period 2071-2079, the frequencies for all discharge grades are greater than period 19902000. When daily peak discharge is greater than 2,500cfs, the frequencies for period 2071-2079 are much larger than that for historical period. 104 40000 35000 Discharge (cfs) 30000 25000 20000 observed 1990-2000 15000 simulated 2031-2040 Simulated 2071-2079 10000 5000 0 0.01 0.1 1 Percent of days exceeded (%) 10 100 Figure 5.13 Percent of daily peak discharge exceeded certain discharge for observed and simulated periods Table 5.3 Average times of daily peak flow greater than certain discharge for one year of each period Time period >800 1990-2000 observed (days) 3.55 1990-2000 simulated (days) 3.27 2031-2040 simulated (days) 3.70 2071-2079 simulated (days) 5.11 Discharge (cfs) >5000 >10000 0.82 0.36 >1500 2.36 >2500 1.36 >20000 0.09 >30000 0.00 2.09 1.55 0.91 0.45 0.18 0.00 3.20 2.20 1.90 0.80 0.30 0.00 4.00 3.67 2.33 1.11 0.11 0.11 5.4 Conclusions and Discussion This research used a physical based rainfall-runoff model to route bias-corrected RCM climate data to identify possible changes in flood magnitude and frequency for the 105 Santa Cruz River basin. Through the use of precipitation data derived from the historical (1990-2000) and future (2031-2040, 2071-2079) RCM data; the annual maximum discharges, daily maximum discharges, and hourly discharges were obtained from the watershed model for the listed three periods. These data were then compared with the observed data for the historical period and put into the context of flood magnitude and frequency analysis. Flood discharges for different return periods increased when considering climate change for the future, the discharge of 100-year return period flood increases by 3,000cfs, and the discharge of 200-year return period flood increases by 5,000cfs. Annual maximum discharge results indicate both flood magnitude and frequency increase for period 2031-2040 and flood magnitude and frequency of middle and low flow (flow less than 12,000cfs) increase for period 2071-2079 period 2071-2079. Daily maximum discharge results show the increase of magnitude and frequency for period 2031-2040 and period 2071-2079 compared with period 1990-2000. Since the study area is located in the dryland, large flood events are seldom occurred. When estimating the flood frequency using annual peak flow data, the lack of large event can lead to uncertainty in the large flood estimation. A continuous long term run would be ideal to reduce sample error. At present, this possibility is limited by the computer power, but could be more feasible with future computing improvements. 106 CHAPTER 6 SUMMARY, CONCLUSIONS AND FUTURE RESEARCH 6.1 Summary and Conclusions The objective of this study is to simulate unsteady flow and sediment transport in vegetated channel network and apply a two-dimensional surface flow routing model to study the impact of climate change on flood magnitude and frequency. Chapter 1 is the literature review of related studies and the objective of this dissertation. In Chapter 2, the governing equations for one-dimensional and twodimensional hydrodynamic and sediment transport models are presented. The numerical schemes to solve the governing equations, the Godunov-type finite volume method, were briefly described here. Chapter 3 is the detailed description of the one-dimensional unsteady flow and sediment transport model for vegetated channel networks. The modified St. Venant equations together with the governing equations for suspended sediment and bed load transport were solved simultaneously to obtain flow properties and sediment transport rate. The Godunov-type finite volume method was employed to discretize the governing equations. Then, the Exner equation is solved for bed elevation change. Since sediment transport is non-equilibrium when bed is degrading or aggrading, a recovery coefficient for suspended sediment and an adaptation length for bed load transport are used to quantify the differences between equilibrium and non-equilibrium sediment transport rate. The influence of vegetation on floodplain and main channel was 107 accounted for by adjusting resistance terms in the momentum equations for flow field. A procedure to separate the grain resistance from the total resistance was proposed and to calculate sediment transport rate. The model was tested by a flume experiment case and an unprecedented flood event occurred in the Santa Cruz River, Tucson, Arizona, in July 2006. Simulated results of flow discharge and bed elevation changes showed satisfactory agreements with the measurements. This part of 1-D modeling study concludes: 1. In vegetated channel, flow resistance includes grain resistance, bed form resistance, vegetation resistance, and side wall resistance. As vegetation density increases, vegetation resistance increases, so flow resistance increases. 2. The increase of vegetation resistance will reduce the grain resistance that transports bed load sediment. The denser the vegetation, the less the sediment transport. 3. The grain resistance rather than the total resistance should be used in sediment transport model for calculating sediment transport rate. A new method to separate grain resistance from the total resistance is presented in this study. The 2nd part of this research is to apply the two-dimensional surface routing model, CHRE2D, to SCRW, which is detailed in Chapter 4. The vegetation influence was considered by using the modified Manning’s coefficient that takes account of the vegetation coverage. The vegetation coverage was extracted from satellite photos, 108 although the accuracy remains to be verified. The CHRE2D model was calibrated using the observed data at the Cortaro Gauge on the Santa Cruz River. In Chapter 5, flood magnitude and frequency change were estimated by using the RCM climate outputs. Hourly precipitation data derived from the RCM-for three periods (1990-2000, 2031-2040 and 2071-2079) were used as input data for the calibrated CHRE2D model for predicting the impact of climate change on magnitude and flood frequency. The Santa Cruz River Watershed located in the Southern Arizona was chosen as the study area. Precipitation output in the study area from RCM-WRF was biascorrected using the observed gridded precipitation data for 1990-2000. The scaling factors obtained from historical periods were applied for two future periods to correct the bias of hourly precipitation data. The watershed model was calibrated and then used to simulate flood routing for three periods. Simulated annual and daily maximum discharges and hourly discharges are obtained and analyzed for the above three periods. Conclusions regarding the impacts of climate change on flood frequency curve are: 1. Flood discharges for different return periods increased by considering future climate change, the discharge of 100-year return period flood increases by 3,000cfs, and the discharge of 200-year return period flood increases by 5,000cfs. 2. Annual maximum discharge results indicate both flood magnitude and frequency increases for period 2031-2040, while the magnitude of small flood increases and the frequency of large flood decreases for period 2071-2079. 109 3. Daily maximum discharge results show the increase of both magnitude and frequency for period 2031-2040 and 2071-2079 compared with period 1990-2000. 6.2 Future Research Results from this study showed vegetation has significant influence on flow and sediment transport, and this influence can be quantified by using 1D and 2D models. An accurate and reliable 2D surface flow model is capable of supplementing additional data for flood frequency analysis. Future research will be focused on the experiment and numerical study of interactions among vegetation, flow and sediment transport; twodimensional surface flow routing with sediment transport. Vegetation plays an important role for flow routing and sediment transport in both floodplain and riparian area. The resistance to flow through vegetated area increases and the mean velocities reduces comparing to the non-vegetated area. However, sediment transport may be increased as the vegetation coverage is sparse due to the perturbation and turbulence vortex induced by vegetation stems, branches and leaves. Intensive researches have been conducted on the flow resistance force caused by vegetation; but few studies have reported the interaction of vegetation and sediment transport. The mechanism of sediment transport in vegetated channel needs further investigation. 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