Development and application of a raster based stormwater simulation model

Abstract Objectives of this research are: 1 to develop a raster-based stormwater simulation model with capacities of modeling not only surface runoff flow but also underground pipe flow

Dissertation

Development and Application of a Raster-based

Stormwater Simulation Model

（ラスター型雨水シミュレーションモデルの開発とその応用）

Submitted by Chau Nguyen Xuan Quang

Dissertation submitted to the Department of Civil and Environmental Engineering of Nagaoka University of Technology in partial fulfillment of the requirements for the

Degree of Doctor of Engineering

Committee Members:

Prof Minjiao Lu (Chairman) Associate Prof Toshiro Kumakura Associate Prof Tokuzo Hosoyamada Associate Prof Atsushi Rikimaru Associate Prof Guangwei Huang (External Examiner)

Nagaoka, Japan, March, 2008

Abstract

Objectives of this research are: (1) to develop a raster-based stormwater simulation model with capacities of modeling not only surface runoff flow but also underground pipe flow and handling the spatial variability of hydrologic parameters

in fine scale (2) to improve the quality of rainfall estimated from weather radar by using neural network (3) to develop a simple and efficient filter method for removing non-ground measurement points of raw laser altimetry data (4) to apply the raster-based stormwater simulation model for inundation analysis and inundation mitigation planning in Kamedagou basin, Niigata Prefecture, Japan

The raster-based stormwater simulation model is designed to operate surface rainfall runoff modeling on watershed data discretized into square raster elements of desired spatial resolution Surface runoff is generated at each raster element and routed to the inlets of the drainage channel network by using two-dimensional diffusion wave approximation The one-dimensional dynamic wave, EXTRAN model (the hydraulic component of SWMM), was adopted for describing drainage channel network flow The output of the proposed model is not only hydrograph at inlets and basin outlet but also the water depth on ground surface The simulated surface water depth can be used to establish the flood risk map

The raster-based stormwater simulation model is ideally suited for use with radar rainfall which is a crucial input for hydrologic modeling in ungauged or poorly gauged basins However, uncertainty largely limits the applicability of radar rainfall

in hydrologic modeling In this research, a neural network was trained to establish the relationship between the radar reflectivity (Z) and ground rainfall measurement (R) at raingauge sites Then, the radar rainfall estimated by using the trained neural network (RNN) over the basin is applied for hydrologic modeling by using distributed hydrologic model in order to evaluate the performance of the trained

technique is more appropriate method for radar rainfall estimation than the existing operational Z-R relationship The network trained at the rain gauge sites is accurate, stable, and robust for estimating radar rainfall over the basin

Highly accurate topography should be used for flood inundation modeling Recently, high quality DEM can be generated from the laser altimetry data To generate high quality DEM from laser altimetry data, a progressive slope-based filter method was successfully developed to remove the non-ground measurement points from laser altimetry data In the proposed filter method, the new method was proposed for removing the blunder points of the raw laser altimetry data The progressive approach was also introduced to speed up the filter process The new filtering method was successfully applied for laser altimetry data processing in Kamedagou basin The comparisons of simulated results respectively obtained from laser-DEM and conventional DEM indicated that laser-DEM provides better simulation results than the conventional DEM

The proposed model was successfully applied to reproduce the flood on 04, August, 1998 in Kamedagou basin with promised results The results showed that simulated water level and inundation extents are well agreement with the observed ones The well-calibrated raster-based stormwater simulation model was applied to inundation mitigation planning The simulated results suggested that further construction of drainage channel network in the highly urbanized areas, the northern part of Kamedagou basin, and increasing of pumping rate approximates 60m3/s are necessary to mitigate inundation in this area

v

Acknowledgements

This research received tremendous helps, encouragements and appreciation of many individuals and organizations Firstly, I would like to express my deep gratitude to Professor Minjiao Lu for his guidance, supports, and encouragements throughout the duration of this research

Grateful acknowledgements are made to Associate Professor Toshiro Kumakura, Associate Professor Tokuzo Hosoyamada and Associate Professor Atsushi Rikimaru for serving as Examination Committee Members Their constructive criticisms and suggestion were of invaluable help in conducting this research

The author is deeply indebted and honored that Associate Professor Guangwei Huang of the University of Tokyo, a well known scholar in his field, kindly agreed to serve as the External Examiner

The financial support of the Japanese Government through a scholarship award is gratefully acknowledged Pursuing the doctoral program at the Nagaoka University

of Technology would have been impossible without this financial support I also extend my thanks to the Niigata city government for their helps in data sharing

I am thankful to my friends, Dr Yamamoto Takahiro and Mr Kamimera Hideyuki, for their helps and supports during working at Lab of Meteorology and Hydrology Many thanks also go to my Vietnamese friends at Nagaoka University of Technology for their helps in various ways

I would finally like to thank my family as they always kept sending good wishes and encouragements I also extend my thanks to my two young sisters and their husbands for their assistance to my parents and my grandparents while I was away The last but not the least my deepest gratitude goes to my wife, Ms Le Thi Thu Ha, for her support and love

Chapter 2 Development of a raster-based stormwater simulation model

2.3.4 Linkage of surface flow and channel flow 17

3.4 Simple description of the distributed hydrologic model 28

3.5.1 Performance evaluation criteria 29 3.5.2 Development of the trained neural network 30 3.5.3 Radar rainfall estimation results 31 3.5.4 Hydrologic modeling results 33

Chapter 4 A progressive slope based filter method for laser altimetry data processing

4.3 Progressive slope based filter method 41 4.4 Laser altimetry data processing 47

Kamedagou Basin 4.5 Generation of Digital Elevation Model 52

List of figures

Figure Content Page

2.2 Representation of impervious part and pervious part 9

2.3 Illustration of depression storage depth in each grid cell 11

2.4 Schematic description of overland flow routing 12

2.5 Conceptual representation of the EXTRAN module 17

2.6 Description of inflow and outflow at nodes 18

2.7 Illustrating of flow interaction at node 19

3.1 A typical multilayer feedforward network 23

3.3 Accumulative basin-average rainfall of six flood events 33

3.4 Comparisons of the observed hydrographs versus the

simulated hydrographs of six flood events 35

4.1 Framework of progressive slope based filter method 43

4.2 Illustration of blunder points filtering assumption 45

4.3 Illustration of moving direction and step of scanning window 46

4.4 Illustrating for the blunder points removing 48

4.5 The measurement points after filtering steps 48-50

4.6 Numbers of points was removed versus window sizes 50

4.7 Illustrating of the measurement points that can not remove 51

4.8 The ground measurement points obtained after filtering 51

4.9 Digital Elevation Model generated from bear-ground point 52

4.10 Digital Elevation Model generated from laser data 53

Laser_DEM)

5.3 Drainage channel network, study raingauge, pumping station

5.5 Relationship between water level and storage volume of

5.10 Comparison of simulated and observed water level at Takeoba 63

5.12 Simulated and observed water level at Toyanokata 64

5.15 Comparison of simulated and observed inundation areas 66 5.16 Comparison of simulated water levels obtained from

conventional DEM and laser-DEM at Manjo gate 66 5.17 Comparison of simulated discharges obtained from

conventional DEM and laser-DEM at Manjo gate 67 5.18 Comparison of simulated water levels obtained from

conventional DEM and laser-DEM at Takeoba 67 5.19 Comparison of simulated discharges obtained from

conventional DEM and laser-DEM at Takeoba 68 5.20 Comparison of simulated water levels obtained from

conventional DEM and laser-DEM at Toyanokata 68 5.21 Comparison of simulated discharges obtained from

conventional DEM and laser-DEM at Toyanokata 69

5.23 Simulated water level at Takeoba in case of adding 60 m3/s at

5.24 Simulated water level at Toyanokata in case of adding 60 m3/s

5.25 Maximum simulated water depth in case of adding more

pumping capacity of 60m3/s at Oyamatsu pumping station 71

List of tables

Table Content Page

3.2 Illustration of the training and testing data set domains 30

3.3 Statistical comparison results of radar rainfall estimation at the

training gauge group (R05-R06- R07-R09-R10-R11-R14)

32

3.4 Statistical comparison results of radar rainfall estimation at the

testing gauge group (R08-R12-R16)

32

3.5 Statistical comparison results of hydrologic modeling 35

3.6 Total of observed and simulated discharge of six flood events 36

Chapter 1 Introduction

1.1 Problem statements

Stormwater simulation model is a useful tool for planning, design, operation, and management of drainage network system As a planning and design tool, the model’s result can be used to estimate size, location, and capacity of the drainage network system As an operation tool, the stormwater simulation model is used to real-time control of facilities of drainage network such as tidal gate, pumping station As a management tool, the model’s result can be used to analyze and compare the strategies in practical management Because of above importance, various numerical models have been developed to simulate stormwater process such as Storm Water Management Model (SWMM) (Huber and Dickinson, 1988), MOUSE (Lindberget

al., 1989), and Illinois Urban Drainage Simulator (ILUDAS) (Terstriep and Stall,

1974), etc

In general, available stormwater simulation models often consist of two main components: the hydrologic component and the hydraulic component The hydraulic component of these available models is powerful for hydraulic simulation of drainage channel network However, the hydrologic component of these models is insufficiently powerful to describe the spatial variability of surface rainfall runoff process The hydrologic component of these models is enhanced in order to handle the spatial variability of hydrologic parameters at very fine scale

Recently, urban floods are more serious due to the increasing of number of heavy rainfall Flood disaster often causes high damage in urban areas because high

population, industrial site located in urban areas Flood modeling is necessary for prediction and reduction of flood damage in urban areas Flood modeling can predict the flood prone areas It will help to reduce the severe impact of flooding on the resident Incorporating advanced surface flood flow model into stormwater simulation model is carried out for effective stormwater management

Application of radar rainfall for hydrologic modeling has been carried out for many years The accuracy of rainfall estimated from radar reflectivity is still a challenge for the hydrologist Although radar rainfall is highly uncertainty, it is useful for hydrologic modeling in ungauged or rare gauged basin Improvement of the performance of Z-R relationship of weather radar (where Z is radar reflectivity and R is ground rainfall) has been studied in many researches Neural network is found to be appropriate for establish the Z-R relationship because its capacity of modeling highly non-linear relationship

Quality of Digital Elevation Model (DEM) is one of significant important factors for successful hydrologic modeling, especially raster-based distributed modeling Effect of DEM accuracy on hydrologic modeling has been evaluated in many researches (Kenward et al., 2000; Stephen, 2000; Dutta et al., 2001) The DEM accuracy strongly affects on the hydrologic features and simulation results The hydrologists highly expect to obtain the high quality of DEM for their applications

Recently, airborne laser altimetry has been become a prime method for directly measuring of surface features and properties of the landscape for over large area The DEM generated from the laser altimetry data is expected to have high quality because the laser altimetry can measure elevation of the terrain surface at high point density The laser altimetry data is three dimensional point clouds This data includes the measurement points of ground surface and measurement points of non-ground objects like trees, bushes, or buildings, etc Therefore, before generating the DEM, it needs to separate the non-ground measurement points from the laser altimetry data Various automation methods have been developed for laser altimetry processing (Vosselman, 2001 and Zhang et al., 2003) However, a simple and efficient filtering method is still necessary for laser altimetry data processing

1.2 Objectives of the research

The objectives of the research are:

• to develop a raster-based stormwater simulation model which is capable of modeling not only surface runoff flow but also underground pipe flow

• to improve quality of rainfall estimated from weather radar by using neural network

• to develop a simple and efficient filtering method for removing non-ground measurement points from raw laser altimetry data

• to apply the raster-based stormwater simulation model for inundation modeling and inundation mitigation planning in Kamedagou basin, Niigata Prefecture, Japan

Chapter 2 Development of a raster-based stormwater simulation model

2.1 Introduction

Up to now, various numerical models have been developed to simulate stormwater process such as Storm water management model (SWMM) (Huber and Dickinson, 1988), MOUSE (Lindberg et al., 1989), Illinois Urban Drainage Simulator (ILUDAS) (Terstriep and Stall, 1974), etc Structure of these models

generally consists of two models: the hydrologic model and the hydraulic model The hydrologic model simulates the conversion process of rainfall to surface runoff The hydraulic model describes the flow in drainage network and flow on ground surface

In these models, the hydrologic process is separated conceptually from hydraulic process Surface runoff hydrographs are computed for each sub-catchment and then they are used as an input for hydraulic model

The hydrologic component of available stormwater simulation models commonly uses a sub-catchment structure to represent the study watershed Spatial variability of hydrologic parameters is achieved by dividing a study catchment into many sub-catchments Using sub-catchment structure, it can setup and calibrate the hydrologic model easily However, this structure may cause several limitations when applied in urban areas The practical application showed that subcatchment separation is a difficult task because subcatchment boundary is not usually clear in urban areas, especially in flat areas In addition, human development causes significant modifications to catchment and flow paths The land surface is highly heterogeneous Thus, detailed spatial variability of hydrologic parameter is necessary for urban area However, in the models that used sub-catchment structure, the spatial variability of

hydrologic parameters could not be handled in detail like using the raster structure as the previous researches (Smith, 1993 and Julien et al., 1995) In addition, the sub-catchment based approach is insufficient capacity to output the flow rate and water depth at desired points in the watershed interior

To overcome the limitations of sub-catchment structure, the raster structure is recommended to perform hydrologic modeling in stormwater simulation model The stormwater simulation model using raster structure is ideally suited for using with rainfall that is estimated from the weather radar Further more, modeling of stormwater quality and erosion is required for stormwater quality management in urban areas The raster structure is a useful platform for integrating stormwater quality and erosion modeling into stormwater simulation model

Recently, inundation has been frequently occurred in urban areas due to the increasing number of heavy rainfall events Management and planning of inundation

in urban areas have become an important issue Various numerical models have been developed to simulate flood inundation (Connel et al., 2001; DiGiammarco et al., 1996) However, these models considered only overland flow and channel flows on ground surface The flow in underground network is ignored, although it is significant to highly urbanized areas On the other hand, available stormwater simulation models are insufficient capacity in analysis of the surface overland flow Therefore, modeling of overland flow is required in order to take into account entire complex phenomenon of urban drainage This can provide a more useful platform for determining exactly the locations of flood prone areas as well as the design deficiencies of the drainage system, especially in highly urbanized settings

Several major efforts have been directed at integrated surface/ storm sewer modeling by linking hydrodynamic storm sewer and surface flow models Hsu et al (2000) integrated two-dimensional diffusion wave surface model into dynamic wave stormwater model The surface runoff is generated by using RUNOFF module of SWMM The purpose of two-dimensional diffusion wave is to describe the flooding flow when the flow exceeds the transportation capacity of drainage network But, in this research, the spatial variability of hydrologic parameters is still handled by using

sub-catchment structure Smith (1995) proposed a GIS-based distributed parameters hydrologic model for urban areas The hydrologic parameters were handled by using raster structure But this model was insufficient to simulate the facilities on drainage

network system such as weir, pumping, storage reservoir, etc…, although they are

very important for comprehensive simulation of drainage network system

2.2 Model description

A raster-based stormwater simulation model is designed to operate on watershed data discretized into square raster elements of desired spatial resolution The proposed model can simulate both overland flow and underground flow The proposed model also has capability of simulating facilities on drainage network system

There are several basic assumptions for hydrologic modeling in the raster-based stormwater simulation model as bellow:

• surface runoff is a Hortonian process

• once water is lost from the surface to infiltration, it does not reappear

• parameters within each cell element are homogeneous

• flow depth and discharge rate are considered uniform on individual cells

• the cell that contains node (inlet) is referred at drainage cell

A physical model, Green-Amp model, is used to generate surface runoff at each raster element Each raster element contains the information on surface elevation, roughness coefficient, infiltration parameters, percentage of impervious area, and depression storage depth The generated runoff at the raster element is routed to the inlets/manholes of drainage channel network by using two-dimensional hydraulic model The hydraulic process in the drainage channel network is performed by using the EXTRAN module, a component of the Storm Water Management Model (SWMM) The input flow rate at inlets is calculated by using weir equation when the surcharge does not occur at this inlet and it set to zero when the surcharge occurs at this inlet Detailed description of the linkage of surface flow and channel flow is presented in section 2.3.4 The surcharge outflow rate from the drainage channels is

estimated from EXTRAN model The proposed model is capable of simulating both surface flow and underground pipe flow Figure 2.1 presents the framework of the raster-based storm water simulation model:

Figure 2.1 Framework of the raster-based stormwater simulation model

2.3 Governing equations

The four major components of the raster-based stormwater simulation model are presented in this section Those components include surface runoff generation, overland flow routing, channel flow routing, and linkage of surface flow and channel flow The surface runoff generation component simulates the transformation of rainfall to surface runoff These four major components are combined to become a complete stormwater simulation model

2.3.1 Surface runoff generation

The inverse distance method is adopted to interpolate the distribution of rainfall intensity over the watershed The interpolated equation is:

surface runoff estimation

update surcharge from previous time

step at drainage cells

overland flow routing

calculate inlet discharge

open channel/ underground flow routing

start

end

)k,j(i)k,j(

where i(j, k) is the rainfall intensity at cell(j, k) (mm/hr)

in(jrg, krg) is the rainfall intensity at cell(jrg, krg) that raingauge located (mm/hr)

dm is the distance from cell(j, k) to nth raingauge located at cell(jrg, krg) (m)

nrg is total number of rain gauges

In urban areas, land surface involves impervious area and pervious area

Impervious area includes road, building, roof, parking lot, concrete surface, etc

Impervious area and pervious area are mixed together Therefore, in computation, it

is assumed that the land surface of each grid cell containing its own fraction of pervious and impervious sub-areas as illustrated in Figure 2.2

Figure 2.2 Representation of impervious part and pervious part

For each grid cell, the runoff is generated for pervious part and impervious part respectively It is assumed that there is no runoff drains from pervious area to impervious area and vice versa In the impervious area, the runoff equals to the rainfall intensity because infiltration quantity in this area is too small In the pervious area, the runoff equals to rainfall intensity after subtracting infiltration loss The surface runoff of each grid cell equals to total runoff generating from pervious part and impervious part

Impervious part

Pervious part Represent to

Infiltration is process that water penetrates into the ground surface The infiltration quantity can be estimated by using empirical model or physical model The benefit of physical model is that the model requires shorter historical hydrologic data for model calibration than empirical model Therefore, in the proposed model, the Green and Ampt model is adopted to estimate the infiltration rate and cumulative infiltration depth for each grid cell in the study watershed By neglecting the level of ponding on the surface, the general equation showing the Green-Ampt relationship can be expressed as (Bras, 1990):

where f is the infiltration rate (m/s)

F is the cumulative infiltration depth (m)

Su is the average capillary suction at the wetting front (m)

IMD is the initial moisture deficit (m/m)

Ks is the saturated hydraulic conductivity (m/s)

Parameters of Eq.(2.2) are generally obtained through soil type of each grid cell The soil type is reclassified for each grid cell Their numerical values can be obtained

from the experimental data by Rawls et al (1983) depending on the soil texture.

Mein and Larson (1973) presented the two-stage model to calculate the infiltration rate from Green-Ampt model If the cumulative infiltration volume (F) is less than the cumulative infiltration volume required causing surface saturation (Fs), the infiltration rate equals rainfall intensity If Fs > F, the infiltration rate predicts directly

by Green-Ampt equation, Eq.(2.2)

The cumulative infiltration volume required for causing surface saturation (Fs) is:

1 K /

IMD S F

long time steps By substituting f = dF/dt into Eq.(2.2) and integrated to obtain:

) C F ln(

C F ) C F ln(

C F ) t t (

Ks 2− 1 = 2− 2+ − 1+ 1+ (2.4)

where C = IMD.S (m), t is time (s),

1,2 is subscripts for the start and the end of time interval respectively

The Eq.(2.4) is solved by using Newton-Raphson method to find F2, the cumulative infiltration at the end of the time step

2.3.2 Overland flow routing

Overland flow occurs when the water depth in the grid cell exceeds the depression storage depth as illustrated in Figure 2.3

Figure 2.3 Illustration of depression storage depth in each grid cell

Routing of the overland flow between adjacent cells can performs by using dimensional or two-dimensional hydraulic model By using one-dimensional hydraulic model, a flow path network has to pre-determine This approach is useful for region where the slope is steep because it is simple and requires less computation time However, in flat urban areas, pre-define of a network of interconnected channels is extremely difficult In this case, the two-dimensional hydraulic model is more appropriate to perform flow simulation Previous researches (Collins et al., 1999; Bishop et al., 1999) have pointed out that two-dimensional modeling of floods has a number of advantages over one-dimensional modeling (Boonya-Aroonnet et al., 2002) and quasi-two-dimensional (Molinaro et al., 1994) modeling

one-Depression storage depth d(m)

Width (m)

Length (m)

In this study, overland flow routing proceeds in a two dimensional cascading manner from cell to the cell or cells downstream as depicted in Figure 2.4

Figure 2.4 Schematic description of overland flow routing

The governing equations for overland flow routing are based primarily on the Saint Venant Equations of continuity and momentum The general form for these equations, as shown in Julien, P Y and Saghafian, B (1991), are commonly expressed in partial differential form as:

de-Continuity:

qy

qx

qx = unit flow rate in x direction

qy = unit flow rate in y direction

q = generated surface runoff (rainfall intensity – losses)

The momentum equation is derived by equating the net forces per unit mass to the acceleration of flow The differential form of the momentum equation in the x and y

Inlets

direction is expressed as:

uvx

uvx

In the diffusion wave approximation, the local and convective acceleration terms

on the left side of equations (2.6) and (2.7),

y

uvx

uut

u

∂

∂+

∂

∂+

∂

∂

are assumed to be

negligible, and those equations are reduced to the following:

n

y , x

) y , x (

The equations of two-dimensional diffusion wave are solved by using the explicit finite difference scheme For a given cell(j,k) at time t, the following first order approximation of the continuity for two-dimensional flow is applied:

tW

)j1j(q)1jj(qW

)k1k(q)1kk(qq)k,j(h

t y

t x

t x t

=

∆

(2.13)

where: )ht ∆ t( ,jk is flow depth at cell(j,k) at time t+∆t

)k,j

(

ht is flow depth at cell(j,k) at time t

∆t is computation time step

q is surface runoff rate

)1kk

(

S

t t

The unit discharge is computed from the following formulation of the Manning equation:

For x-direction:

2 / 1 t

2 / 1 t

t

)1k,j(n

)]

k1k(S[)k1

t

)k,j(n

)]

k1k(S[)k1

2 / 1 t

t

y [h (j 1,k)]

)k,1j(n

)]

j1j(S[)j1

t

)k,j(n

)]

j1j(S[)j1

2.3.3 Channel flow routing

In this study, EXTRAN (EXtended TRANsport), a module of SWMM, is adopted

to describe the flow in the drainage channel network In EXTRAN module, a node concept is used for representation of drainage network The conceptual overview of this approach is shown as Figure 2.5 The conduit network is idealized

link-as series of links which are connected at nodes Inflows (inlet hydrographs) and outflows (surcharges) of EXTRAN module are taken place at nodes

Fig 2.5 Conceptual representation of the EXTRAN module

EXTRAN module can perform flow routing both branched and looped network of open and/or closed channel It has capacity of simulating the following elements: pipes, manholes, weirs, orifices, pumps, storage basins, and outfall structures Further more, this model can simulate backwater effect, reverse flow in the drainage channel because the flow routing is performed by the dynamic wave The governing equations are:

0 x

Q t

∂

∂ +

∂

0 gAS x

H gA x

) A / Q ( t

Q

f

2

= +

∂

∂ +

∂

∂ +

g is the gravitational acceleration (m/s2)

H is the hydraulic head (m), and Sf is the friction slope

An explicit finite different method is used to solve these equations Detailed numerical schemes could be found in the model’s manual (Huber and Dickinson, 1988)

2.3.4 Linkage of surface flow and channel flow

The surface flow and channel flow is exchanged through the inlets of the drainage

channel network The surface runoff drains into the storm sewer network though the inlets as shown in Figure 2.6(a) The drainage channel network transports these flows

to the basin outlet During transportation process, if the actual discharge exceeds the design discharge of conduit, the flow surcharges through inlets onto ground surface

as shown in Figure 2.6(b)

Figure 2.6 Description of inflow and outflow at nodes There are several assumptions for modeling of bi-directional flow at nodes:

• the cell contains node is referred as drainage cell

• surcharge is collect to atop of node with the storage area is equal area of drainage cell

• crown elevation of node set equal to elevation of drainage cell

Figure 2.7 illustrates the linking of overland flow and underground flow

Surface runoff

WL

WL Surcharge flow

Outflow Inflow

(a)

(b)

Figure 2.7 Illustration of flow interaction at node

where,

dov is overland depth (m)

dsur is surcharge depth (m)

dx is size of drainage cell (m)

Zfull is full depth of node (m)

Znode is depth of node at time t (m)

Vnode is volume of node at time t (m)

It is assumed that the surface runoff only flows into the inlet if the inlet is at surcharge stage in previous computation time-step The inflow discharge contribute

non-to inlet is calculated by using the weir equation as Eq.(2.22)

5 1 ov w

w inlet k L gd

g is gravitational acceleration (m2/s)

dov is flow depth (m)

If the inlet was surcharged in last time-step, the inflow set to zero However, the water depth at drainage cell (cell that contains node) affects to the flow in underground pipes Therefore, Znode and Vnode have to be updated as following equations

Znode = Zfull + dov (2.23)

Vnode = dov*dx*dy (2.24) The surcharge outflow from node is determined from EXTRAN module by using Preissman slot concept Detailed description of this computation is presented in the model’s manual (Huber and Dickinson, 1988)

2.4 Summary

The raster-based stormwater simulation mode has been proposed for simulating the stormwater in urban areas The proposed model handles the hydrologic parameters in raster format The model performs simulation of both overland flow and underground flow Further more, the model has capability of simulating the facilities on the drainage network system The output of the proposed model is not only the hydrograph at basin outlet, nodes but also the water depth at each raster elements The information on water depth during simulation time is used to create the inundation map for study areas

Chapter 3 Neural network-based radar rainfall estimation

3.1 Introduction

Uncertainty largely limits the applicability of radar rainfall in hydrologic modeling despite of its large areal coverage with high spatial and temporal resolution Krajewski and Georgakakos (1985) showed that the error of radar rainfall could be as large as about fifty percent Recent application of radar rainfall in hydrologic modeling indicated that the simulated results derived from radar rainfall are less

accurate than those obtained from gauge rainfall (Johnson et al., 1999; Sun et al., 2000; Yang et al., 2003 and Neary et al., 2004) Clearly, the accuracy of hydrologic

modeling using gauge rainfall strongly depends on rain gauge density in the study basin The accuracy of the simulated results decreases at the basins with a low density of rain gauges In the basins with a dense gauge network, the hydrologic modeling is solely based on the gauge rainfall On the contrary, in the ungauged or poorly gauged basins, the radar rainfall input can be an alternative for hydrologic modeling Despite of the given uncertainty, therefore, radar rainfall is still a crucial input for hydrologic modeling in ungauged or poorly gauged basins

The rainfall intensity (R) is estimated from the radar reflectivity (Z) by using the power law of the form Z = BRβ (known as Z-R relationship), where B and β are parameters The Z-R relationship was pioneered by Marshall and Palmer (1948) The performance of radar rainfall estimation mainly depends on a proper choice of Z-R relationship (Anagnostou and Krajewski, 1998) Various methods have been proposed to improve the accuracy of radar rainfall estimation One of the successful approaches was the neural network based radar rainfall estimation method (Xiao and

Chandrasekar, 1997) In this approach, the neural network was employed to establish

a relationship between the radar reflectivity (Z) and the ground rainfall intensity (R) The neural network was appropriately trained by using the historical data of radar reflectivity and gauge rainfall measurement at the rain gauge sites as input and output

of the network respectively It was concluded that, at the rain gauge sites, the radar rainfall products derived from the trained network are more accurate than those obtained from several existing Z-R relationships However, the accuracy of the neural network based radar rainfall product at the full areal coverage of the radar, which is very important for distributed hydrologic modeling, is unable to be determined due to the lack of the ground truth rainfall data for comparison It is recognized that the distributed hydrologic modeling using the radar rainfall input

estimated by the trained network (hereafter R NN) evaluates not only the impact of

RNN input on the accuracy of simulated results, but also it is a useful step for implicitly examining the performance of the trained network at the basin scale

The objective of this chapter is to investigate if the streamflow modeling with the

RNN input could yield a more accurate result than that using the radar rainfall input

derived from the existing Z-R relationship (hereafter R Z-R) Further more, we also seek to examine the comprehensive performance of the trained network at the basin scale In this study, more attention is paid to the comparison of the results between two radar rainfall products (RNN and RZ-R) rather than the comparisons of the results between gauge and radar rainfall The conclusions were assessed by the statistical results of comparison between the estimated radar rainfall products and between the observed hydrographs and the simulated ones which were obtained from gauge

rainfall (hereafter R G), RNN, and RZ-R respectively The hydrologic data of six flood events in the Uono River basin was used to verify the research methodology

3.2 Methodology of neural network based radar rainfall estimation

3.2.1 Introduction of neural network

A neural network is a massively parallel-distributed information processing system inspired from our understanding of biological neural processing Although various paradigms of neural network have been developed in the literature (i.e

Multilayer Feedforward Network (MLFN), Radius Basis Function (RBF), Recurrent Network (RN)), the MLFN trained with the well-known Backpropagation (BP) algorithm is found to be simple and efficient for establishing the nonlinear relationship between input and output in many cases Therefore, in this study, the MLFN and the BP algorithm were selected to approximate the highly nonlinear relationship between radar reflectivity and ground rainfall intensity

MLFN is a common neural network consisting of one input layer, one output layer and more than one hidden layers of neurons The neurons from one layer have weighted connections with neurons in the next layer, but no connection between neurons in the same layer A typical MLFN is shown as Figure 3.1

Figure 3.1 A typical multilayer feedforward network

The net input k

j

n to node j in layer k can be obtained from:

k j 1 k i m

1 i

k , 1 k ij

W I 13

b III 22

b III 11

b II 33

b II 22

b II 11

b I 33

b I 22

b I 11

Output 2 Output 1

Input 2

Input 1

W I 23

W III

W III

W III

W II 33

W II 11

W I 11

Output Layer Input Layer

W I 12

W I 22

W II 12

W II 13

W II 21

W II 22

W II 23

W II 31

W II 32

W III

W III

W III

where m k-1 is the number of nodes in layer k-1, k

b is the bias of node j in layer k

The sigmoid function is most frequently used to compute the output k

j

o from node

j in layer k in case of nonlinear relation modeling as showing in previous research

(Chau, 2004) Therefore, the output k

j

o is computed as:

) n exp(

1

1 )

n (

j

k j

2 j

j o t 2

The adjustment value of weight, w k , k ( i )

∆ − , and bias, b k ( i )

∆ , within the progress of training are defined as:

) s ( w o

) 1 s (

wijk−1,k + = ηδkj ik−1+ α ∆ kij−1,k

∆

(3.4)

) s ( b o

) 1 s (

l layer output at )

o t )(

o 1 ( o

1

m 1 i

1 k j 1 k , k ij j j

j j j j k

3.2.2 Neural network based radar rainfall estimation

Neural network based radar rainfall estimation consists of two stages, the development stage and the application stage As for the development stage, there are two periods namely the training period and testing period The training period establishes the relationship of radar reflectivity and rainfall intensity through the training process The testing period verifies the performance of the trained network After the network is well trained at the calibration gauge sites, it is ready for the application stage The trained network is applied to estimate the radar rainfall for full areal coverage of radar

For development of a trained neural network, three main steps including network architecture selection, data processing, and network training are carried out as following

3.2.2.1 Network architecture selection

Although the proper choice of neural network architecture significantly affects the accuracy of the result, there are no common rules for this selection Decisions must

be made regarding aspects such as the number of input and output variables, the number of the hidden layers and the nodes within hidden layers Aside from the

output variables, which are the same as the desired outputs, the other selections are mainly based on trial and error, and developer’s experiences

The output of the network is hourly measured gauge rainfall The input of the network and the network architecture are determined by several training experiments For the input selection, the radar reflectivity (Z) and the radar rainfall product (RZ-R) are tried as input for training the network in turn The radar reflectivity (Z) is the hourly mean value at the grid cell which covers the measured gauge sites The radar rainfall products (RZ-R) are converted from the Z-R relationship (RZ-R = (Z/B)1/β) by using the operational and optimal parameters of B and β, respectively

3.2.2.2 Data processing

The available data set was divided into two separate data sets, the training data set and the testing data set The training data set was used to train the network The trained network was verified its performance by using the testing data set

The data is normalized using following formula before applying for neural network training

05.0a

A

)aR(9.0

.0

)05.0r)(

aA(

where R i is the actual value, r i is the transformed value, a and A is the minimum and

maximum value of the time series of input data respectively

3.2.2.3 Network training

When the training data and network architecture was determined, the training process was implemented to obtain the optimal connection weights and biases This process was repeated until the error of both the training and testing periods satisfied a

target error or number of iterations exceeded the given epochs The training process will also be prematurely stopped to avoid the ‘overfiting’, a phenomena where the performance of the training period increases but the performance of testing period decreases

3.3 Study basin and data

The study basin, the Uono River basin is located in the northern part of Japan, Figure 3.2 The main stream of this basin is the Uono River, a tributary of the Shinano River which is the longest in Japan The basin is hilly with an elevation ranging from 100m to about 2000m and a drainage area of about 355 km2 The study area is completely covered by the Yakushidake weather radar The spatial and temporal resolutions of this radar are three kilometers and five minutes, respectively

Hydrologic data of six flood events, including five-minute radar reflectivity data, hourly measured rainfall (at ten gauges located inside and nearby the study basin as shown in Figure 3.2), and hourly observed discharge at the basin outlet were used in this study The names of ten raingauges are Muikamachi (R05), Ikasawa (R06) Shimizu (R07), Futai (R08) Tuchitaru (R09), Yuzawa (R10), Miyanoshita (R11), Miyamura (R12), Gomisawa (R14), and Ohmine (R16) Detailed description of six flood events is presented in Table 3.1 Though five-minute radar reflectivity data is available, the hourly simulation was performed because the conventional data of measured rainfall and discharge are hourly measurements

Table 3.1 List of the selected flood events

Figure 3.2 Map of the Uono River basin

3.4 Simple description of the distributed hydrologic model

A distributed hydrologic model developed by Lu et al (1996a) was applied for the Uono River basin (detailed description of this model refers to Lu et al (1996a)) The basin was divided into 36,233 grid cells of 100mx100m (slightly larger than officially published drainage area 355km2) The runoff from the grid cells are calculated by using the conceptual rainfall runoff model, XinAnJiang model, (Zhao, 1992) The generated runoff of a grid cell is considered to concentrate immediately

to its center and to flow to one of its eight neighbor cells forming the steepest slope The flow path between these two grid points (the center of a grid cell) is modeled as

an open rectangular channel Hence the runoff of grid cells can be routed to the basin outlet through this channel network The flow routing in the channel network is computed by kinematic wave approximation In order to keep the downstream

Ikasawa Gomisawa

channel to be routed after the routing of all its upstream channels, Lu et al (1993, 1996b) developed an automatic algorithm to determine the optimal routing order of channel network In this study, the model parameters are calibrated by using the

gauge rainfall data and are applied to simulation using other rainfall data sources

3.5 Results and discussion

3.5.1 Performance evaluation criteria

The following criteria were used to evaluate the performance of radar rainfall estimation and hydrologic model output

Correlation coefficient (Coef):

2 i i n

1 i

2 i i

n 1

i i i i i

) S S ( ) O O (

) S S )(

O O (

2 i

n 1 i

2 i i

) O O (

) O O ( 1

2 i

i S ) O ( n

1

mean observed value, and n is number of data points

3.5.2 Development of the trained neural network

The available data set was divided into two separate data sets, the training data set and the testing data set The training data set includes four flood events no 890806,

890918, 900919 and 901007, of seven training gauges namely R05, R06, R07, R09, R10, R11, and R14, which were randomly chosen from ten gauge sites The testing data set includes two other remaining flood events 940929 and 950915 of seven training gauges and all of six flood events at three other remaining gauges, namely R08, R12, and R16 The domains of training and testing data sets are illustrated in Table 3.2 The selection of testing data ensured that the performance of the trained network can be tested both spatially and temporally

Table 3.2 Illustration of the training and testing data set domains

Flood events Rain

R) is derived from optimal parameters (B and β) is not quite different with the network trained with the RZ-R is obtained from the operational parameters This is because of the optimization ability of neural network While the accuracy of two