UNIVERSITY OF HAWAIII LIBRARY

UNIVERSITY OF HAWAIII LIBRARY

HYDROLOGICAL ANALYSIS FOR SELECTED WATERSHEDS ON O'AHUISLAND IN HAWAI'I

A THESIS SUBMITTED TO THE GRADUATE DIVISION OF THEUNIVERSITY OF HAWAI'I IN PARTIAL FULFILLMENT OF THE

REQillREMENTS FOR THE DEGREE OF

MASTER OF SCIENCE

IN

CIVIL ENGINEERING

August 2003

By

Tsung-I Liao

Thesis Committee:

Michelle H. Teng, ChairpersonEdmond D. H. Cheng

Pao-Shin ChuPhilip Ooi

ACKNOWLEDGEMENTS

I would like to take this opportunity to express my gratitude to my professors and

friends who have helped me during my studies. Dr. Michelle H. Teng's enthusiasm,

detailed instruction, and insight guidance throughout my research is greatly appreciated.

Dr. Edmond D.H. Cheng's masterful hydrologic knowledge provides me with

constructive opinions toward my thesis. Dr. P.S. Chu's guidance about the rainfall data

source and analysis and Dr. P. Ooi's comments are very valuable in helping me to present

my thesis in an understandable way. I truly appreciate their assistances.

I would like to thank Mr. Greg H. Hiyakumoto from R.M. Towill Corporation for

his instruction toward my work. Special thanks go to my parents, my girlfriend Jung

Sheng Lee, my friends Mr. Edison Gica, Mr. Gavin Masaki, Mr. Matthew Fujioka, Ms.

Wendy Chen, and Mr. Jian Ping Uu for their care, patience, and support throughout my

studies.

This thesis is funded in part by a grant from the Federal Highway Administration

and the Hawaii State Department of Transportation Project No. HWY-L-2000-05

(Contract No. 46509).

iii

ABSTRACT

This thesis focuses on hydrological study of selected watersheds on the Island of

Oahu, Hawaii. The study includes rainfall frequency analysis for six selected rain gages

situated within different watersheds, namely, Hawaii Kai Golf Course 724.19, Kailua

Fire Station 791.3, Kahuku 912, Makaha, Pupukea Height 896, and Waimea 892. Runoff

prediction based on three different methods for Kamananui Stream found within Waimea

Watershed is also presented in this study. The GIS/ArcInfo software package is used in

this study as a supporting tool.

For rainfall frequency analysis, Gumbel Distribution and Log Pearson Type III

Distribution for extreme values are applied to predict the return intervals of different

rainfall intensities based on 24-hour duration for the selected watersheds according to

long-term hourly rainfall data that were available up to year 2002. The calculated results

are compared with the predictions from two earlier studies published in 1962 and 1984.

The objective is to examine the effect of newer and longer rainfall data on the frequency

analysis results. Our results show that the rainfall intensity of different return intervals

predicted in the present study using the newer and longer data records in general agrees

quite well with the results predicted by the two earlier studies. A further study on the

effect of record length on the accuracy of rainfall frequency prediction is carried out and

the results show that the average error in predicting rainfall frequency based on 15-year

and 20-year records is similar to that based on longer records (e.g., 30- and 40-year

records), however, longer records provide more consistent predictions with smaller

uncertainty. This result confirms that for predicting a value of return period Y based on

the Gumbel distribution, a data record longer than OAY years (40% of recorded data) is

iv

preferable. In the present study, intensity-duration-frequency (IDF) curves are also

developed for Kaelepulu and Waimea Watersheds based on long-term I5-minute rainfall

data. The conversion factor for converting I-hour rainfall intensity to rainfall intensity of

other periods based on the IDF curves is determined. The present result is compared with

the empirical conversion factor used in engineering design. Our results show that there

are some noticeable differences between the empirical values and the actual values of the

conversion factor as indicated in the City and County of Honolulu Storm Drainage

Standards Manual. However, the differences are relatively small and the empirical factor

is acceptable for engineering practice.

For stream runoff prediction, three different methods, namely, the rational

method, the Soil Conservation Service's (SCS) (now known as Natural Resources

Conservation Service (NRCS» TR-20 method, and the USGS regression method, are

used to predict runoff amounts for gaged Waimea Watershed. The objective of this part

of the study is to examine the consistency and validity of the three different methods for

predicting stream flow in Hawaii. Our results show that all three methods give quite

consistent predictions for runoff of different return periods in Waimea Watershed despite

the fact that the area of the watershed is relatively large and exceeds the upper limit for

the area for the rational method. The predicted runoff results also show good agreement

with the measured results based on the stream gage record.

v

TABLE OF CONTENTS

ACKNOWlEDGEMENTS .iii

ABSTRACT .iv

TABLE OF CONTENTS vi

LIST OF TABLES viii

LIST OF FIGURES xi

CHAPTER 1. INTRODUCTION 1

1.1 Technical Background 1

1.2 "Literature Review 6

1.3 Objective of the Present Study 9

CHAPTER 2. RAINFALL FREQUENCY ANALySIS 11

2.1 Description of Raw Data 11

2.2 Gumbel Distribution 14

2.3 Log Pearson Type III Distribution 30

2.4 Annual Series and Partial Series 42

2.5 Intensity-Duration-Frequency Curves 43

2.6 Effect of Record Length on Accuracy of Prediction 63

CHAPTER 3. COMPARISON AMONG THREE DIFFERENT METHOIDS FOR

PREDICTION OF STREAM DISCHARGE 67

3.1 Description of Waimea Watershed and Kamananui Stream 67

3.2 Commonly Used Methods for Predicting Stream Flow 68

VI

3.2.1 Soil Conservation Service Technical Release-20 (TR-20) 68

3.2.2 United States Geological Survey (USGS) Regression Method 77

3.2.3 Rational Method 82

3.3 Peak Discharge from Stream Gage Record in Waimea Watershed 86

3.4 Stream Flow Prediction by Applying the SCS TR-20 Method 90

3.5 Stream Flow Prediction by Applying the USGS Regression Method 95

3.6 Stream Flow Prediction by Applying the Rational Method 96

CHAPTER 4. SUMMARY AND CONCLUSION 101

APPENDIX A. DETAILED RESULTS OF SENSITIVITY ANALYSIS 104

APPENDIX B. TR-20 INPUT FILE FOR WAIMEA WATERSHED 108

REFERENCES , 109

vii

LIST OF TABLES

Table Page

Table 2.1 Summary of Raw Data Records 14

Table 2.2 Gumbel Distribution Frequency Factors, KT 18

Table 2.3 Summary of a and b Parameters of Each Rain Gage Station 18

Table 2.4 Summary of Maximum Daily Precipitation 18

Table 2.4 Summary of Maximum Daily Precipitation, Continued 1 19



Table 2.5 Average and Standard Deviation of Each Rain Gage Station 21

Table 2.6 Error Limits for Flood Frequency Curves 21

Table 2.7 Gumbel Distribution Results for Hawaii Kai GC 724.19 Versus R-73 and

TP-43 22

Table 2.8 Gumbel Distribution Results for Kahuku 912Versus R-73 and TP-43 22

Table 2.9 Gumbel Distribution Results for Kailua fire Station 791.3 Versus R-73 and

TP-43 22

Table 2.10 Gumbel Distribution Results for Makaha Versus R-73 and TP-43 23

Table 2.11 Gumbel Distribution Results for Pupukea Heights 896.4 Versus R-73 and

TP-43 23

Table 2.12 Gumbel Distribution Results for Waimea 892 Versus R-73 ,and TP-43 23

Table 2.13 Logarithm Parameters of Each Rain Gage Station 33

Table 2.14 Log Pearson Type III Results for Hawaii Kai GC 724.19 Versus R-73 and

TP-43 40

Vlll

Table 2.15 Log Pearson Type III Results for Kahuku 912Versus R-73 and TP-43 .40

Table 2.16 Log Pearson Type ill Results for Kailua fire Station 791.3 Versus R-73 and

TP-43 40

Table 2.17 Log Pearson Type ill Results for Makaha Versus R-73 and TP-43 .41

Table 2.18 Log Pearson Type ill Results for Pupukea Heights 896.4 Versus R-73 and

TP-43 41

Table 2.19 Log Pearson Type III Results for Waimea 892 Versus R-73 and TP-43 .41

Table 2.20 Comparison between Gumbel distribution and Log Pearson Type ill

Distribution in Predicting 100-year, 24-hour Storm ..42

Table 2.21 Empirical Factors for Converting Annual Series to Partial Series .43

Table 2.22 Sample Data before Adding More IS-Minute Intervals 45

Table 2.23 Sample Data after Adding More IS-Minute Intervals 46

Table 2.24 Maximum IS-Minute Duration Rainfall For Kailua Fire Station 791.3 47

Table 2.25 USGS Mean Order Method .48

Table 2.26 IDF Curves Summary, Waimea 892 51

Table 2.27 IDF Curves Summary, Kailua Fire Station 791.3 52

Table 2.28 Correction Factor, Waimea 892 60

Table 2.29 Correction Factor, Kailua Fire Station 791.3 61

Table 2.30 Comparison between the Actual and Predicted 80-year Rainfall for Waimea

892 Rain Gage and Kahuku 912 Rain Gage Stations 65

Table 3.1 USGS Regression Equations, Region 1 Leeward, Oahu 78

Table 3.2 USGS Regression Equations, Region 2 Windward, Oahu 79

Table 3.3 USGS Regression Equations, Region 3 North, Oahu 79

ix

Table 3.4 Criteria for Using Regression Equations on Oahu 80

Table 3.5 Runoff Coefficients for Built-Up Areas, Rational Method 83

Table 3.6 Frequency Factor, Rational Method .

...... 84

Table 3.7 Annual Peak Discharge for USGS Stream Gage Station 16330000 88

Table 3.8 Frequency Analysis for USGS Stream Gage Station 16330000 88

Table 3.9 Time of Concentration Calculation - SCS TR-20, Waimea Watershed 94

Table 3.10 Predicted Peak Discharge - SCS TR-20, Waimea Watershed 94

Table 3.11 Predicted Peak Discharge - USGS Regression Equations, Waimea Watershed

...........................................................................................95

Table 3.12 Predicted Peak Discharge - Weighted USGS Regression Equations, Waimea

Watershed 96

Table 3.13 Time of Concentration Calculation - Rational Method, Waimea Watershed

............................................................................................98

Table 3.14 Predicted Peak Discharge - Rational Method, Waimea Watershed 99

x

LIST OF FIRGURES

Figure

Figure 1.1 Distributions of Rain Gages on Oahu, Hawaii .4

Figure 1.2 Distributions of Stream Gages on Oahu, Hawaii 5

Figure 2.1 Selected Rain Gage Stations on Oahu 13

Figure 2.2 Hawaii Kai Golf Course 724.19, Gumbel '" 24

Figure 2.3 Kahuku 912, Gumbel. , 25

Figure 2.4 Kailua Fire Station 791.3, Gumbel. 26

Figure 2.5 Makaha, Gumbel '" 27

Figure 2.6 Pupukea Heights 896.4, Gumbel.. 28

Figure 2.7 Waimea 892, Gumbel. 29

Figure 2.8 Hawaii Kai Golf Course, Log Pearson Type III 34

Figure 2.9 Kahuku 912, Log Pearson Type III 35

Figure 2.10 Kailua Fire Station 791.3, Log Pearson Type III 36

Figure 2.11 Makaha, Log Pearson Type III 37

Figure 2.12 Pupukea Heights 896.4, Log Pearson Type III 38

Figure 2.13 Waimea 892, Log Pearson Type III.. . .. . .. .. . .. .. .. . .. .. . .. . .. . .. .. .. . .. 39

Figure 2.14 IDF Curves, USGS Mean Order Method, Waimea 892 53

Figure 2.15 IDF Curves, Gumbel Distribution, Waimea 892 54

Figure 2.16 IDF Curves, Log Pearson Type III, Waimea 892 55

Figure 2.17 IDF Curves, USGS Mean Order Method, Kailua fire Station 791.3.... . 56

Figure 2.18 IDF Curves, Gumbel Distribution, Kailua Fire Station 791.3 57

Xl

Figure 2.19 IDF Curves, Log Pearson Type Ill, Kailua Fire Station 791.3 58

Figure 2.20 Correction Factor Plot. 62

Figure 3.1 Waimea Watershed on Oahu 68

Figure 3.2 TR-20 Computation Sequence 69

Figure 3.3 Geographic Boundaries for SCS Rainfall Distributions 72

Figure 3.4 Average Velocity for Shallow Concentrated Flow 76

Figure 3.5 Hydrologic Regions, Oahu, Hawaii 78

Figure 3.6 Runoff Coefficients for Agricultural and Open Areas, Rational Method 85

Figure 3.7 Location of USGS Stream Gage Station 16330000 in Waimea - Part 1 87

Figure 3.8 Location of USGS Stream Gage Station 16330000 in Waimea - Part 2 87

Figure 3.9 Frequency Analysis for USGS Stream Gage Station 16330000 89

Figure 3.10 Land Use Condition - Waimea Watershed 91

Figure 3.11 Illustration of Weighted Curve Number. 92

XlI

CHAPTER 1. INTRODUCTION

1.1 Technical Background

In engineering design of hydraulic structures such as bridges across rivers,

culverts for highways, dams, and detention ponds for flood-control, an important design

parameter is the stream discharge under different flood frequencies. For gaged streams,

flow discharge of different return periods can be determined based on statistical analysis

of past stream flow records. For un-gaged streams, the flow discharge can only be

determined indirectly by studying past records of rainfall intensity first. Once the

probability of the rainfall intensity is calculated, certain empirical approaches (e.g., the

rational method, Soil Conservation Service's TR-20 method, and the USGS regression

method) can be used to predict peak flow of different frequency based on the rainfall

information. Hydrologic analysis is the branch of study in water resources engineering

that involves the statistical analysis of past rainfall and stream records and the prediction

of stream flow either based on past flow data or through empirical means based on the

rainfall data.

Due to the fact that hydrologic studies depend heavily on statistical and empirical

analysis, universally valid equations for predicting rainfall and stream flow do not exist.

Even if the equations may appear to have the same mathematical expressions, the values

for the parameters involved in the equations must be calibrated and verified for each local

region or even each watershed. In the state of Hawaii, government agencies such as US

Geological Survey (USGS) and National Oceanic and Atmospheric Administration

1

(NOAA)'s National Weather Service (NWS) have maintained many rain and stream

gages distributed at different locations in Hawaii for many decades (see Figures 1.1 and

1.2). The recorded data can be very helpful in hydrologic analysis. On the other hand, we

have also noted that not all streams in Hawaii are gaged. Even for those gaged streams,

many of the gages are located near the upstream reaches of the streams. Since in Hawaii,

many major highway bridges and culverts are located at the downstream end, i.e., near

the stream mouth entering the ocean, directly recorded data for flood discharge near the

downstream outlet are not available.

In previous rainfall frequency analysis, the local engineers depended mainly on

the rainfall atlas presented in Technical Paper No. 43 (TP-43) published by the U.S

Department of Commerce, Weather Bureau in 1962. This report provides rainfall

frequency maps that can be used when planning and designing hydraulic structures in

Hawaii. About 20 years later, the rainfall atlas was updated for the Island of Oahu in

Technical Report R-73 published by the State of Hawaii, Department of Land and

Natural Resources in 1984. Since then, twenty more years of new rainfall data have

become available. However, the rainfall atlas has not been updated since the last report

was released in the early 1980s. There has been a great interest from scientists as well as

government and private engineers in examining the accuracy and applicability of these

earlier references by studying longer and newer rainfall data records and deciding

whether an update of the rainfall atlas for Hawaii is necessary. Part of this thesis study

will perform rainfall frequency analysis for selected watersheds on Oahu for such

purposes.

2

For prediction of stream flow, there exist several methods that can be applied.

These include the rational method, the regression method, the Soil Conservation

Service's TR-20 or TR-55 methods, and the routing method. All the methods use rainfall

data as part of the input. They also require the information on land cover, topographical

slope, drainage area and other information for estimating the stream flow of different

return period. In Hawaii, currently, there is not one preferred method by all scientists or

engineers. For example, the hydraulic design section of the State Department of

Transportation uses the regression method while some private consulting firms (e.g.,

R.M. Towill, personal communication) apply the SCS's TR-20 method. It is of interest to

conduct a comparative study to examine the accuracy, efficiency and consistency of

different methods for predicting flood discharge in streams in Hawaii.

This thesis study is part of a research project funded by the Federal Highway

Administration through the Hawaii State Department of Transportation to study the

problem of bridge scour during floods and the problem of sand plugging of highway

bridges and culverts at selected streams on Oahu. In order to predict bridge scour and

sand plugging, stream flow of different flood frequencies must be determined first for

each selected stream. The present thesis is focused on hydrologic analysis of rainfall

frequency and on determining the best suitable method for predicting flood discharge for

watersheds and streams on Oahu.

3

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VI

Figure 1.2 Distributions of Stream Gages on Oahu, Hawaii

1.2 Literature Review

The pioneering systematic research on rainfall frequency analysis of the Hawaiian

Islands was conducted by the U.S. Department of Commerce, Weather Bureau in the

early 1960s. It produced a very useful report entitled "Technical Paper No. 43 Rainfall

Frequency Atlas of the Hawaiian Islands for Areas to 200 Square Miles, Durations to 24

Hours, and Return Periods from 1 to 100 Years". It was published in 1962 as a request

from the Soil Conservation Service (SCS). A total of 287 stations with standard 24-hour

gages recorded precipitation amounts once per day. The last recorded precipitation data

available for TP-43 was 1959, which was as accurate as the data permitted at the time

during the project periods. All rainfall data were compiled to perform a frequency

analysis. As the results of the project work, rainfall frequency maps were provided for the

entire State of Hawaii to assist engineers obtaining rainfall depths according to specific

request of duration and return periods.

Another major systematic research on rainfall frequency analysis for Hawaii was

conducted by Dr. Giambelluca at the University of Hawaii in the 1980s. The publication

was entitled "Rainfall Frequency Study for Oahu, Report R-73". As suggested in TP-43,

new analysis should be considered if more than 10 years of additional precipitation data

were collected. Thus, a cooperative effort among the State of Hawaii, Department of

Land and Natural Resources and University of Hawaii's Water Resources Research

Center was sought. Their efforts were to update the rainfall frequency maps presented in

TP-43 for the Island of Oahu. With more than 20 years of new precipitation data

available, R-73 superseded TP-43. Precipitation records from a total of 156 rain gages on

Oahu were used in R-73. However, TP-43 was still valid for other islands of the state

6

since it had statewide coverage. No significant update of the rainfall frequency analysis

for any of the Hawaiian Islands has been conducted since the release of R-73 report in

1984 until recently when Professor P.S. Chu at the University of Hawaii, Department of

Meteorology is updating the maps. This gap has raised some questions in the scientific

and engineering community in Hawaii: are the results published in 1962 and 1984 still

applicable? About twenty more years of rainfall data have become available. If we add

these new data into the analysis, will they provide more accurate prediction for the

rainfall frequency? Is it necessary to update rainfall frequency every ten to twenty years

as some of the earlier studies suggested?

For flood discharge frequency analysis, various models are available to predict

peak flow. Commonly known models are: the Soil Conservation Service TR-20 computer

program, the USGS regression equations, and the rational formula. The TR-20 model can

assist engineers in determining flood hydrographs and route through channel and

reservoirs. Hydrographs can be then combined from the main stream and its tributaries,

and peak discharges can be computed. The program was first developed by the

Hydrology Branch of the Soil Conservation Service (SCS) in cooperation with the

Hydrology Laboratory Agricultural Research in 1964. It was written in FORTRAN

computer language, which initially ran only on IBM mainframe computers. The

Engineering Division of SCS later made several modifications over the years to improve

the program capability. A PC version with draft user manual was released in 1986, and

further revisions were made in 1992.

The regression method, which correlates basin and climatic characteristics with

flood magnitudes, is another commonly used method in Hawaii. Wu (1967) was the first

7

person in Hawaii to develop the regression method for flood study on Oahu. Two

regional formulas were presented for the 100-year flood events as the results. Nakahara

(1980) further refined Oahu into three regions and came out with newly updated

formulas. The latest regression equations for Oahu were provided by Wong (1994).

The rational method, which has been adapted by the City and County of Honolulu

in the Storm Drainage Standards since 1959, is another popular method. It correlates flow

rates with rainfall intensity and drainage areas. Rainfall intensity is usually obtained from

known IDF Curves (Intensity-Duration-Frequency Curves). These curves require detailed

statistical analysis of 15-minute (or even higher resolution) rainfall records and

significant effort to produce. For the state of Hawaii, the IDF curves for most of the

watersheds are not available. An approximation to an actual IDF curve is to use the

available hourly rainfall information (e.g., from TP-43 and R-73 depending on the data

availability and accuracy) and then convert it into rainfall intensity of shorter or longer

durations through an empirical conversion factor whose values were proposed in the

studies in the 1950s and 1960s. In the Storm Drainage Standards, the rational method is

used for drainage areas of 100 acres or less. For watersheds whose areas are larger than

100 acres, the Storm Drainage Standards provides additional guidance for the prediction

of stream flow in these larger watersheds. It should be mentioned that even though the

latest edition of the Storm Drainage Standards for Honolulu was published in 2000, most

of the information in the manual was from the earlier years of the 1950s and 1960s,

except the rainfall frequency analysis results which have been updated based on the 1984

R-73 report.

8

1.3 Objectives of the Present Study

This thesis study is part of an initiation research project entitled "Instrumentation

and Monitoring of Sand Plugging and Bridge Scour at Selected Streams in Hawaii"

funded by the Federal Highway Administration and the Hawaii State Department of

Transportation. The thesis study will not attempt to answer all unsolved questions but

rather will focus on studying several questions related to rainfall frequency analysis and

the prediction of stream flow of different flood frequencies. It is hoped that the results

from this study will be helpful to local government agencies and private consulting firms

in their hydraulic design, and it may also have some scientific values in hydrologic

analysis in general.

Specifically, the objectives of this thesis are to:

1. Conduct statistical analysis of rainfall data updated to year 2002 for selected

watersheds on Oahu; predict rainfall frequency based on Gumbel and Log

Pearson Type ill Distributions and compare the results with the earlier results

published in 1962 and 1984; determine whether twenty more years of data will

change the earlier statistical results, and determine the minimum length of data

records that is sufficient for predicting rainfall frequency reliably

2. Develop IDF curves for selected watersheds on Oahu based on updated rainfall

data in order to examine the validity and accuracy of the Ihr-to-other duration

conversion factor obtained in studies 40-50 years ago.

3. Predict stream flow under different flood frequencies by applying three different

methods including the rational method, the SCS's TR-20 method and the USGS

regression method for a selected gaged watershed, and compare the predicted

9

results with the recorded results in order to evaluate the accuracy, efficiency and

consistency of different methods in predicting stream flow in Hawaii

10

CHAPTER 2. RAINFALL FREQUENCY ANALYSIS

In this chapter, we will present the results of rainfall frequency analysis at

selected rain gage sites on Oahu. The length of the records ranges from 28 to 83 years,

and the data are as updated as to year 2002. The results from the present analysis are

compared with those reported in TP- 43 (1962) and R-73 (1984). The main objective is

to examine whether twenty or forty more years of data would predict different results

compared with the previous publications. In addition, the effect of rainfall data record

length on the accuracy of frequency prediction is investigated.

2.1 Description of Raw Data

The first important step for any frequency analysis is data collection. To ensure

the results will yield higher accuracy, long-term data should be collected as completely as

possible. For this study, rain data are obtained from the National Climatic Data Center

(NCDC) website. Six rain gage stations (Figure 2.1) scattered over the Island of Oahu are

selected as a case study. Rainfall data in I5-minute, hourly, and daily format are used in

the analysis.

Data obtained through NCDC are from two types of rain gages. One is a standard

gage, and the other is an autographic gage. Data in I5-minute and hourly formats are

recorded from autographic gages, and the daily total precipitation amounts can be

calculated as the summation of hourly values. For a standard gage, it only provides one

daily precipitation value for a fixed time interval. For some rain gage stations, there may

exist data taken from both rain gage types in a certain time period. Daily totals from

11

different types of gages may differ from each other. There are two reasons that may

explain the differences. The first is because the values are measured by two different

gage types, where the measurement mechanism may be different. The second reason is

caused by the measurement time when precipitation values are taken. A standard gage

only records value once per day either in the early morning or late afternoon while an

autographic gage takes values on an hourly basis starting from midnight (per calendar

day).

Because standard gages are read once per day, the data itself represents an

observation from a fixed interval. It is possible that the true maximum 24-hour rainfall

may occur between two observations. As a result, the standard gage may not catch the

real peak rainfall value. Weiss (1964) applied a theoretical approach to provide an

adjustment factor of 1.143 for converting a fixed-interval reading to an actual reading for

daily rainfall. The application of the adjustment factor was adopted by both TP-43 and R

73 reports. For an autographic gage, it is not necessary to apply the adjustment factor

since the hourly measurement is sufficient to catch the true 24-hour rainfall. Therefore,

the value taken from autographic gage is considered as a true-interval value in this study.

The raw data summary is listed in Table 2.1. Hawaii Kai Golf Course 724.19 rain gage

station actually consists of two sets of hourly precipitation records. One set is called

Hawaii Kai GC 724.19, COOPID 518665, and its record period is from January 1974 to

August 1977. The other set is also called Hawaii Kai GC 724.19, but with a different

COOPID assigned as 511308. Its record period is from September 1977 to October 2002.

These two sets of data can be considered as one station since both stations have the same

latitude and longitude coordinates, but with a slight difference in elevation. Similarly, this

12

assumption can be applied to Makaba Station, whose record is the combination of three

sub-records, namely, Makaha Valley 800.1, Makaha Pump 800.2, and Makaha Country

Club 800.3, to form a continuous record. For Pupekea Heights 896.4 rain gage station,

the record is the combination of Pupukea, Pupukea Farm, and Pupukea Heights records.

For rain gage station Kahuku 912, data in Year 1975 are missing. The six rain gages are

chosen in this study based on two reasons: 1) the rain gages are well distributed over the

island to be better representatives of the island rainfall condition, and 2) these rain gages

have more detailed rain records (daily and hourly).

Pupukea Heights 896.4

Waimea 892

Kahuku 912

Kailua Fire Station791.3

HawaiiKaiGolfCourse 724.19

13

Table 2.1 Summary of Raw Data Records

Rain Gage StationStandard Gage Autographic GageRecord Record

Hawaii Kai Golf Course 724.19 None 1974-2002 (hourly)Kahuku 912 1919-1964 (daily) 1965-2001 (hourly)Kailua Fire Station 791.3 1959-1964 (daily) 1965-2001 (hourly)Makaha 1958-1965 (daily) 1966-2002 (hourly)Pupukea Heights 896.4 1919-1945 (daily) 1968-2001 (hourly)Waimea 892 1919-1964 (daily) 1965-2002 (hourly)

2.2 Gumbel Distribution

General equation for hydrological frequency analysis is proposed as the following

by Chow (1951):

AT=.A.+KT* S

where

AT =desired rate (rainfall, flow) at particular recurrence interval, T

.A. =average rate (rainfall, flow) of the collected data

(2.1)

KT =frequency factor at particular recurrence interval, T (it varies with chosen statistical

models)

S =standard deviation of the collected data

For Gumbel Distribution, the term KT is defined as follows:

1 TKT =-a +bln[ln(--)] =-a +bln[ln(--)] (2.2)

F(V) T-l

where

a = location parameter dependent on sample size

b =scale parameter dependent on sample size

14

T =recurrence (return) interval or recurrence (return) period

F(V) = Cumulative Density Function (CDF)

Here, a parameter is defined as "Reduced Variate", W, so that equation (2.2) can

be linearized as follows:

TWr =-In[ln(-)]

T-l(2.3)

Substituting (2.3) into (2.1) and (2.2), the final form of Gumbel distribution

equation can be obtained as:

AT=A - (a + b* WT) * s (2.4)

In order to verify whether the sample fits into certain statistical distribution

models, confidence limits or control curves are placed on the frequency curves. Usually it

involves placing two lines called 5% and 95% confidence lines above or below the

theoretical frequency line, and the area between the two confidence lines is defined as the

90% confidence band. The confidence band means that 90% of the data should fall within

the band. If most of the sample data tend to fall outside of the confidence band, then that

statistical distribution should not be used to perform analysis for that particular sample.

For Gumbel Distribution, the confidence lines are defined in the following:

AT(5%) =A - (a + b* WT) * s + S * ErrorT(5%)

AT(95%) =A - (a + b* WT) * S - S * ErrorT(95%)

where

AT (5%) =5% value at particular recurrence interval, T

AT (95%) = 95% value at particular recurrence interval, T

ErrorT (5%) = error limit at 5% level at particular recurrence interval, T

15

(2.5)

(2.6)


The procedure to detennine Gumbel Distribution in the present study and

compare the results with the two previous studies are listed as follows:

1. Identify location and scale parameters for each station according to its sample

size. Number of years of record is equal to sample size. Table 2.3 summarizes the

parameters for each rain gage station.

2. Determine the maximum daily total value (24-hour duration) for each year of each

rain gage station from the daily or hourly rainfall data. Table 2.4 summarizes the

results for each rain gage station. The values provided in Table 2.4 are converted

into true-interval values with the adjustment factor of 1.143 for those fixed

interval values.

3. Calculate average (1\) and standard deviation (s) of the sample for each rain gage

station. The results are summarized in Table 2.5.

4. Use data obtained in step 2, rank them in descending order and apply equation

(2.3) to convert Tinto Reduced Variate, W.

5. Apply equation (2.4) to obtain relationship between theoretical rainfall depths and

W. Here we have to assume various values of T.

6. Obtain rainfall depth readings of 24-hour duration, from TP-43 Rainfall

Frequency Atlas of Hawaiian Islands (1962) and Report R-73 Rainfall Frequency

Study for Oahu (1984) according to the location of each rain gage station.

7. Plot data obtained in Step 4 and 5 (W vs. Rainfall Depths) and compare it with

data from Step 6. A factor is applied to the predicted values to convert annual

16

series to partial series (See section 2.4), and the results are summarized in Table

2.7 to Table 2.12.

8. Determine error limits of 90% confidence band based on the raw data and plot

them for each rain gage station.

To determine a and b for a particular sample size, we need to use equation (2.2)

and interpolate values linearly from Table 2.2 (same table as Table 27.3 from

"Introduction to Hydrology" 4th Edition, page 718). For a particular sample size, we first

choose two random recurrence intervals that will yield two readings (KT) from Table 2.2.

Substituting the values into equation (2.2) will result in two equations for two unknowns

(a and b). Solving the equations, we can obtain one set of value for a and b. The process

is repeated for all possible combinations of two recurrence intervals, and the average

values of a and b are used in the hydrological analysis in this study. Table 2.3

summarizes a and b values for the six selected rain gage stations on Oahu.

To determine error limits of 90% confidence band, values are interpolated linearly

when necessary from Table 2.6 (same table as Table 27.7 from "Introduction to

Hydrology" 4th Edition, page 732). The statistical parameters used in equations (2.5) and

(2.6) are derived from raw data of each rain gage station.

The final results are plotted for each selected rain gage station in the following

pages (page 24-29). The green dots are the data taken from NCDC precipitation records,

and the pink line is the theoretical prediction of Gumbel Distribution. The cyan line

stands for values obtained from Report R-73, and black line represents the values

obtained from Report TP-43. Brown lines represent confidence limits. All the values in

17

the chart have been linearized using the Reduced Variate Method of Gumbel Distribution

as mentioned above.

Table 2.2 Gumbel Distribution Frequency Factors, KT

Sample Recurrence Interval (T)Size 2.33 5 10 20 25 50 75 100 100015 0.065 0.967 1.703 2.410 2.632 3.321 3.721 4.005 6.26520 0.052 0.919 1.625 2.302 2.517 3.179 3.563 3.836 6.60625 0.044 0.888 1575 2.235 2.444 3.088 3.463 3.729 5.84230 0.038 0.866 1.541 2.188 2.393 3.026 3.393 3.653 5.72740 0.031 0.838 1.495 2.126 2.326 2.943 3.301 3.554 5.47650 0.026 0.820 1.466 2.086 2.283 2.889 3.241 3.491 5.47860 0.023 0.807 1.446 2.059 2.253 2.852 3.200 3.446 5.41070 0.020 0.797 1.430 2.038 2.230 2.824 3.169 3.413 5.35975 0.019 0.794 1.423 2.209 2.220 2.812 3.155 3.400 5.338100 0.015 0.779 1.401 1.998 2.187 2.770 3.109 3.349 5.261

Infinity -0.067 0.720 1.305 1.866 2.044 2.592 2.911 3.137 4.900

Table 2.3 Summary ofa and b Parameters of Each Rain Gage Station

Station Name Sample Sizea b

(average value) (average value)Hawaii Kai GC 724.19 29 0.483 -0.902Kahuku 912 82 0.468 -0.837Kailua Fire Station 791.3 44 0.475 -0.870Makaha 45 0.475 -0.869Pupukea Height 896.4 61 0.469 -0.850Waimea 892 84 0.467 -0.836

Table 2.4 Summary of Maximum Daily Precipitation

Maximum Daily Precipitation for Each Year (inches), 24 Hours

Kailua Fire Makaha Hawaii Kai Kahuku Pupukea WaimeaStation Golf Course Heights

1919 - - - 1.98 2.30 2.531920 - - - 2.99 3.86 6.971921 - - - 2.40 5.31 3.541922 - - - 3.60 2.33 3.461923 - - - 5.14 3.17 9.20

18

Table 2.4 Summary of Maximum Daily Precipitation, Continued 1

Maximum Dailv Precipitation for Each Year (inches), 24 HoursKailua Fire Makaha Hawaii Kai Kahuku Pupukea Waimea

Station Golf Course Heights

1924 - - - 6.40 5.19 2.97

1925 - - - 2.29 3.37 2.91

1926 - - - 2.79 1.36 0.97

1927 - - - 17.92 5.72 4.69

1928 - - - 4.57 7.32 7.43

1929 - - - 3.06 3.5 3.711930 - - - 2.72 2.06 4.061931 - - - 2.55 2.23 2.63

1932 - - - 3.83 5.94 8.17

1933 - - - 3.83 5.43 5.66

1934 - - - 2.41 2.19 1.37

1935 - - - 4.55 7.32 11.72

1936 - - - 4.00 4.46 4.341937 - - - 3.54 4.00 3.201938 - - - 5.65 7.03 6.92

1939 - - - 10.42 8.12 11.21940 - - - 7.33 6.86 6.001941 - - - 3.46 3.66 3.831942 - - - 3.63 3.89 2.771943 - - - 6.88 3.26 3.431944 - - - 2.72 4.40 4.711945 - - - 4.97 4.08 6.401946 - - - 3.82 - 4.461947 - - - 1.65 - 4.341948 - - - 5.10 - 2.431949 - - - 6.92 - 9.091950 - - - 7.83 - 6.471951 - - - 4.55 - 5.251952 - - - 3.26 - 4.431953 - - - 2.83 - 2.571954 - - - 8.92 - 7.751955 - - - 3.44 - 3.971956 - - - 5.20 - 13.941957 - - - 4.38 - 8.821958 - 4.08 - 8.77 - 6.71

19


Maximum Daily Precipitation for Each Year (inches), 24 HoursKailua Fire Makaha Hawaii Kai Kahuku Pupukea Waimea

Station Golf Course Heights1959 4.06 2.63 - 3.29 - 3.491960 2.40 2.07 - 3.55 - 2.351961 4.11 2.94 - 2.13 - 2.791962 2.47 5.88 - 6.24 - 9.521963 6.06 6.45 - 4.24 - 7.451964 4.30 5.09 - 3.37 - 6.861965 6.13 5.07 - 6.26 - 4.001966 3.36 3.72 - 3.11 - 4.571967 6.18 2.80 - 2.35 - 4.051968 2.71 3.29 - 2.77 2.40 6.311969 4.79 4.57 - 3.33 3.20 4.601970 4.10 2.67 - 2.15 3.40 6.671971 1.95 3.87 - 3.27 4.10 4.491972 1.37 3.16 - 3.37 1.90 3.201973 2.55 1.83 - 1.7 1.10 1.171974 3.04 4.73 1.11 4.21 3.10 2.911975 6.23 6.51 6.29 Incomplete 0.70 5.081976 2.85 8.07 3.87 0.75 1.70 5.311977 1.70 2.50 1.75 1.56 1.90 1.431978 6.60 6.20 5.80 5.00 5.60 3.001979 5.20 3.40 4.50 2.30 3.10 2.401980 6.70 4.10 5.20 2.50 9.30 10.31981 2.30 1.30 1.80 1.90 5.20 4.401982 4.30 7.60 5.90 6.40 4.70 4.701983 1.00 0.60 1.20 2.00 2.10 1.501984 6.80 3.00 2.30 4.00 3.50 3.401985 7.60 4.60 3.90 3.20 5.10 5.901986 3.70 1.50 2.80 2.00 3.00 2.401987 5.50 6.10 8.80 4.60 6.50 1.701988 4.10 4.00 3.60 3.90 4.90 3.801989 2.90 2.70 3.20 2.50 5.20 3.601990 3.50 4.70 3.70 2.30 5.90 4.701991 4.90 5.80 5.90 11.00 8.60 6.701992 3.60 3.10 2.60 2.40 2.70 2.701993 4.10 1.50 1.60 6.20 3.20 2.20

20


Maximum Daily Precipitation for Each Year (inches), 24 HoursKailua Fire Makaha Hawaii Kai Kahuku Pupukea Waimea

Station Golf Course Heights1994 3.20 5.70 3.20 2.50 6.50 5.101995 2.30 1.40 1.40 2.30 2.60 3.301996 2.80 4.50 3.70 5.30 4.20 6.701997 2.50 6.30 2.70 2.80 3.60 3.601998 0.90 1.00 1.00 2.70 1.10 1.201999 1.60 4.60 1.00 3.30 4.70 5.002000 3.10 3.00 2.10 1.90 4.50 1.802001 4.30 3.20 3.20 2.9 (9/01) 2.1 (9/01) 4.102002 2.60 (10/02) 1.60 (10/02) 2.70(10/02) - - 1.3 (04/02)

Table 2.5 Average and Standard Deviation of Each Rain Gage Station

Hawaii Kai Kailua FirePupukea

GC 724.19Kahuku 912

Station 791.3Makaha Heights

896Average (A) 3.339" 4.096 3.783 3.854 4.143Standard

1.889" 2.527 1.694 1.823 1.976Deviation (s)

Waimea892

Average (A) 4.721" The units for average and standard deviation are inches.Standard

2.582Deviation (s)

Table 2.6 Error Limits for Flood Frequency Curves

Years of Exceedance frequency (%, at 5% level)Record (n) 99.9 99 90 50 10 1 0.1

5 1.22 1.00 0.76 0.95 2.12 3.41 4.4110 0.94 0.76 0.57 0.58 1.07 1.65 2.1115 0.80 0.65 0.48 0.46 0.79 1.19 1.5220 0.71 0.58 0.42 0.39 0.64 0.97 1.2330 0.60 0.49 0.35 0.31 0.50 0.74 0.9340 0.53 0.43 0.31 0.27 0.42 0.61 0.7750 0.49 0.39 0.28 0.24 0.36 0.54 0.6770 0.42 0.34 0.24 0.20 0.30 0.44 0.55100 0.37 0.29 0.21 0.17 0.25 0.36 0.45

0.1 1 10 50 90 99 99.9Exceedance frequency (%, at 95% level)

21

Table 2.7 Gumbel Distribution Results for Hawaii Kai GC 724.19 Versus R-73 and TP-43

Hawaii Kai Golf Course 724.19 (24-hour Duration Rainfall Depth)

T Present R-73 Difference TP-43 Difference

2-yr 3.46 4.5 -23.1% 4.5 -23.1%

lO-yr 6.32 8.5 -25.6% 8.5 -25.6%

50-yr 9.08 12.0 -24.3% 12.0 -24.3%

100-yr 10.26 14.5 -29.4% 13.8 -25.7%

Ave. Diff. (abs) 26% 25%

Table 2.8 Gumbel Distribution Results for Kahuku 912Versus R-73 and TP·43

Kahuku 912 (24-hour Duration Rainfall Depth)


2-yr 4.19 4.5 -6.9% 5.2 -19.4%

lO-yr 7.75 8.0 -3.1% 8.8 -11.9%

50-yr 11.17 10.5 6.4% 12.5 -10.6%

100-yr 12.64 12.5 1.1% 14.8 -14.6%


Table 2.9 Gumbel Distribution Results for Kailua fire Station 791.3 Versus R-73 and TP-43

Kailua Fire Station 791.3 (24-hour Duration Rainfall Depth)


2-yr 4.0 4.7 -14.9% 5.0 -20.0%

lO-yr 6.36 8.5 -25.2% 8.5 -25.2%

50-yr 8.73 11.5 -24.0% 12.5 -30%

100-yr 9.76 12.0 -18.7% 13.0 -24.9%


22

Table 2.10 Gumbel Distribution Results for Makaha Versus R-73 and TP-43

Makaha (24-hour Duration Rainfall Depth)


2-yr 4.06 4.3 -5.6% 4.5 -9.8%

lO-yr 6.62 7.3 -9.3% 8.5 -22.1%

50-yr 9.17 10.3 -11.0% 12.0 -23.6%

100-yr 10.28 11.5 -10.6% 13.5 -23.9%


Table 2.11 Gumbel Distribution Results for Pupukea Heights 896.4 Versus R-73 and TP-43

Pupukea Heights 896.4 (24-hour Duration Rainfall Depth)


2-yr 4.35 5.0 -13.0% 5.2 -16.3%

lO-yr 7.07 8.2 -13.8% 8.5 -16.8%

50-yr 9.77 10.0 -2.3% 1l.5 -15.0%

100-yr 10.94 12.5 -12.5% 13.0 -15.8%


Table 2.12 Gumbel Distribution Results for Waimea 892 Versus R-73 and TP-43

Waimea 892 (24-hour Duration Rainfall Depth)


2-yr 4.90 5.0 -2.0% 5.0 -2.0%

lO-yr 8.45 8.2 3.0% 8.5 -0.6%

50-yr 11.94 10.0 19.4% 11.0 8.5%

100-yr 13.44 12.5 7.5% 13.0 3.4%

Ave. Diff. (abs) 8% 3.6%

23

16

Rainfall Frequency Analysis (Gumbel), Hawaii Kai Golf Coune

• New Raw Data - Gwnbel - R73, 1984 - TP43. 1962 ----- 5% Confidence Band --+- 95% Confidence Band

~

I 14

~ 12.s-C 10g~ 8N

l 6t= 4=4!.s 2

d! 0

-2

-2 -1 o

2yrs

1

5yrs

2

10yrs

3

25yrs 50yrs

4

100 yrs

5

Reduced Variate

Figure 2.2 Hawaii Kai Golf Course 724.19, Gumbel

Rainfall Frequency Analysis (Gumbel), Kahuku 912

.

~

~~~_v"'~

L--~~~ ;;..

~~-.....-- ~~~~~--~~ Return Interval;....~

~~,

\..--- 2 yrs I 5 yrs I 10 l'l"s 25 yrs 50 yr. 100, ,yrs

NV'1

20

18';'J 16'"g 14r;:r 12J~1O

i 8..eo 6=i 4.S 2~

o-2

-2 -1 o 1 2 3 4 5

Reduced Variate

Figure 2.3 Kahuku 912, Gumbel

Rainfall Frequency Analysis (Gumbel), Kailua Fire Station 791.3

TP43. 1962 --- 5% Confidence Band --- 95% Confidence Band I

5

Return Interval

43

10 yrs I 25 yrsI

2

Reduced Variate

14

i' 12'5! 10C='c

8.I:l~N ...2 6

tv !.0'\ !

i 4

~ 2 ...t~

2yrsI

-

1

0~1 0-2

Figure 2.4 Kailua Fire Station 791.3. Gumbel

Rainfall Frequency Analysis (Gumbel), Makaha

16

_ 14;i 12.s-C 10:Ic.a 8~NfIG 6~

tv l:lo......:I ~

4=I 2

0

-2-2 -1 o

2yrs

1

5yrs

2

10 yrs

3

25yrs

Return Interval

-~'--50 yrs I 100 yrs

4 5

Reduced Variate

Figure 2.5 Makaba, Gumbel

Rainfall Frequency Analysis (Gumbel), Pupukea Heights 896.4

[. New Rawl Data - Gumbel - R73, 1984 TP43, 1962 --lIf- 5% Confidence Band -+- 95% Confidence Band ]

14

2

5

Return Interval

4

25 yrs

3

10 yrs

2

5yrs

1

2yrs

o-1

o

-2

-2

";j' 12~

'5.51 10-~g 8.Cl~

N 6~

oSeo 4==&!

.51~

NOC

Reduced Variate

Figure 2.6 Pupukea Heights 896.4, Gumbel

Rainfall Frequency Analysis (Gumbel), Waimea 892

I • New Raw Data -Gumbel -R73, 1984 - TP43, 1962 5% Confidence Band --95% Confidence Band I

16

.... 14

J.s 12--~ 10

.c:I 8~

j 6N C.\0 ~= 4

:=aJ 2

o , ~, 2 yrs 5 yrs I lO,yrs I 25. yrs

-2

-2 -1 0 1 2 3 4 5

Reduced Variate

Figure 2.7 Waimea 892, Gumbel

2.3 Log Pearson Type III Distribution

The second statistical distribution selected to perform rainfall frequency analysis

in this study is called Log Pearson Type ill Distribution. The general equation (2.1) for

hydrological frequency analysis proposed by Chow (1951) is still valid, however instead

of using the arithmetic form, the parameter AT is transformed into logarithm form. Thus,

equation (2.1) becomes:

(2.7)

where

Log (AT) =desired rate (rainfall, flow) in logarithm form at particular recurrence interval,

T

A = average rate (rainfall, flow) of the collected data in logarithm form. All events in the

sample should be converted into logarithm form first, and then determine the

average value of the sample from the logarithm-form events.

KT =frequency factor at particular recurrence interval, T (it varies with the chosen

statistical models). For Log Pearson Type ill, K depends on skewness, Cs of

the sample.

S = standard deviation of the collected data in logarithm form. All events in the sample

should be converted into logarithm form first, and then determine standard deviation

of the sample from the logarithm-form events.

Cs =skewness of the collected data in logarithm form. All events in the sample should be

converted into logarithm form first, and then determine skewness of the sample from

the logarithm-form events.

30

Unlike Gumbel Distribution, there is no need to linearize the parameters. In order

to plot the values, a plotting position must first be established. One of the most

commonly used is the Weibull equation:

P =m/ (n+l)

where

m = the rank of all events in the sample, from the lowest to the highest

n = sample size

P = probability of the event equal to or less than the ranked event

(2.8)

Hann (1977) in his book "Statistical Methods in Hydrology" (page 135) suggests

that when data are ranked from the largest (m =1) to the smallest (m =n), the plotting

position should be equal to I-P. The quantity of I-P can be further expressed as the area

under the normal curve F(z):

z 1 2F(z) =J--e-z /2dz

0.J2n(2.9)

The inverse of standard normal distribution, z, can be determined either from

Appendix B of the book entitled "Introduction to Hydrology, 4th Edition" or from

Microsoft spreadsheet software Excel function "NORMSINVO". The final plotting

position, which will be z, in this study for Log Pearson Type III Distribution is

determined from the spreadsheet function for easy usage purpose.

The 90% confidence band for Log Pearson Type III Distribution is defined in the

following:

Log (AT)(5%) = A+ KT * S +S *EfforT (5%)

Log (AT)(95%) = A+ KT * S - S * EfforT (95%)

31

(2.10)

(2.11)

where

Log (AT)(5%) =5% value in logarithm form at particular recurrence interval, T

Log (AT)(95%) =95% value in logarithm form at particular recurrence interval, T


ErrorT (95%) =error limit at 95% level at particular recurrence interval, T

The procedure to perform Log Pearson Type III Distribution and compare with

the two previous studies are listed in thefollowing steps:

1. Transform all events in the sample to their logarithm values

2. Compute the mean logarithm, A, standard deviation of logarithm, s, and the

skewness of logarithm, Cs, of the sample (Table 2.13)

3. Determine frequency factor, KT, for Log Pearson Type III Distribution. The

value can be interpolated from Appendix B, Table B.2 of "Introduction to

Hydrology, 4th Edition" page 754-755

4. Apply equation (2.7) to obtain Log (AT) at particular return interval

5. Compute antilog of Log (AT) to obtain the final predicted value

6. Obtain rainfall depth readings of 24-hour duration, from TP-43 Rainfall

Frequency Atlas of Hawaiian Islands (1962) and Report R-73 Rainfall

Frequency Study for Oahu (1984) according to the location of each rain gage

station

7. Plot data obtained in Step 5 (z vs. Rainfall Depths) and compare it with data

from Step 6. A factor is applied to the predicted values to convert annual

32

series to partial series (See section 2.4), and the results are summarized in

Table 2.14 to Table 2.19

8. Determine error limits of 90% confidence band based on the raw data and plot

them for each rain gage station

The notations used in Log Pearson Type III Distribution in Figures 2.8-2.13 are

the same as in Gumbel Distribution plotting. The green dots are the data taken from

NCDC precipitation records, and the pink line is the theoretical prediction based on Log

Pearson Type III Distribution. The cyan line represents for values obtained from Report

R-73, and the black line represents for values obtained from Report TP-43. Brown lines

represent confidence limits.

Table 2.13 Logarithm Parameters of Each Rain Gage Station

KailuaHawaii Pupukea

Kahuku Fire Makaha WaimeaKaiGC Heights

Station

Logarithm0.455 0.553 0.530 0.527 0.562 0.610

Average

Logarithm

Standard 0.256 0.220 0.218 0.248 0.235 0.245

Deviation

Logarithm-0.205 0.346 -0.652 -0905 -0.700 -0.335

Skewness

33

HaiDlaU Frequency Analysis (Log Peanon Type III), Hawaii Kai Golf Coune

I • New Raw Data - Log Pearson Type ill -- 5% Confidence Band -+- 95% Confidence Band - R73, 1984 ---TP43, 19621

3

w~

100 yrs'- Return Interval

2

.!

.; 1

1.;. 0

"=.a1.-1~

-2

-3

0.1 1

RainfaU Depths, 24 hours (inches)

10 100

Figun 2.8 Hawaii Kai Golf Course, Log Pearson Type In

Rainfall Frequency Analysis (Log Pearson Type III), Kahuku 912

3

•

5 yrs

2.yrs .,.X " & ! I

T 100 yrs ..- Return Interval

2 "'F 50 yrS

25 yrsIOyrs ~.~----I

-2

~

~ 1

1.;. 0

1~ -1

BYo)VI

-3

a 1 10 100

Rainfall Depths, 24 houn (inches)

Figure 1.9 Kahuku 911, Log Peanon Type III

Rainfall Frequency Analysis (Log Pearson Type III), Kailua Fire Station 791.3

I • New Raw Data -Log Pearson Type III .......... 5% Confidence Band --95% Confidence Band -R73. 1984 -TP43, 19621

3

I"..)0'\

2~

i:> 1..!.;. 0

11,-1~

-2

Return Interval

I- :l 'fl~ I AlX ~Jf I

-3

0.1 1

Rainfall Depths, 24 hours (inches)

10 100

Flpre 2.10 Kailua Fire Station 791.3, Log PearsoD Type In

RaiDfaU Frequency Analysis (Log Peanon Type III), Makaha

[ • New Raw Data -Log Pearson Type lli ---if-S%ConfidenceBand """95% Confidence Band -R73, 1984 ... TP43,19621

w-....l

3

2~

i> 1..!.;. 0

11.-1~

-2

-3

0.1


Figure 2.11 Makaha, Log Peanon Type In

10 100

3

Rainfall Frequen~Analysis (Log Pearson Type III), Pupukea Heights 896.4

I • New Raw Data - Log Pearson Type III --- 5% Confidence Band -+- 95% Confidence Band - R73, 1984 - TP43, 1962 !

2~

.!•> 1-•!~ .;. 0

1~ -1~

riIil

-2

-3

o

100 yrs ...- Return Interval

2Syrs

10

Syrs

1 10Rainfall Depths, 24 hoors (inches)

Figure 2.12 Pupukea Heights 896.4, Log Pearson Type ill

100

Rainfall Frequency Analysis (Log Peanon Type III), Waimea 892

I • New Raw Data - Log Pearson Type ill .........- 5% Confidence Band -'-95% Confidence Band - R73, 1984 , TP43, 1962]

3

W1.0

2 .-~

i> 1';

!.;. 0

11,-1~

-2

-3

100~ Return Interval

O..yrs25 yrs IIOyn Hi~~77£-/---------1

5yrs

o 1


Figure 2.13 Waimea 892, Log Peanon Type m

10 100

Table 2.14 Log Pearson Type III Results for Hawaii Kai GC 724.19 Versus R-73 and TP-43

Hawaii Kai Golf Course 724.19 (24-hour Duration Rainfall Depth)


2-yr 3.31 4.5 -26.4% 4.5 -26.4%

lO-yr 6.04 8.5 -28.9% 8.5 -28.9%

50-yr 8.95 12.0 -25.4% 12.0 -25.4%

100-yr 10.26 14.5 -29.4% 13.8 -25.7%


Table 2.15 Log Pearson Type III Results for Kahuku 912Versus R-73 and TP-43

Kahuku 912 (24-hour Duration Rainfall Depth)


2-yr 3.94 4.5 -12.4% 5.2 -24.2%

lO-yr 7.02 8.0 -12.3% 8.8 -20.2%

50-yr 11.09 10.5 5.6% 12.5 -11.3%

100-yr 13.2 12.5 5.6% 14.8 -1.1%


Table 2.16 Log Pearson Type III Results for Kailua fire Station 791.3 Versus R-73 and TP·43

Kailua Fire Station 791.3 (24-hour Duration Rainfall Depth)


2-yr 4.06 4.7 -13.6% 5.0 -18.8%

lO-yr 6.22 8.5 -27.1 % 8.5 -27.1%

50-yr 7.91 11.5 -31.2% 12.5 -36.7%

100-yr 8.54 12.0 -28.8% 13.0 -34.3%


40

Table 2.17 Log Pearson Type III Results for Makaha Versus R-73 and TP-43

Makaha (24-hour Duration Rainfall Depth)


2-yr 4.16 4.3 -3.3% 4.5 -7.6%lO-yr 6.53 7.3 -10.5% 8.5 -23.2%50-yr 8.13 10.3 -21.1 % 12.0 -32.3%100-yr 8.65 11.5 -24.8% 13.5 -35.9%


Table 2.18 Log Pearson Type III Results for Pupukea Heights 896.4 Versus R-73 and TP-43

Pupukea Heights 896.4 (24-hour Duration Rainfall Depth)


2-yr 4.41 5.0 -11.8% 5.2 -15.2%lO-yr 6.99 8.2 -14.8% 8.5 -17.8%50-yr 8.97 10.0 -10.3% 11.5 -22.0%100-yr 9.69 12.5 -22.5% 13.0 -25.5%


Table 2.19 Log Pearson Type III Results for Waimea 892 Versus R-73 and TP-43

Waimea 892 (24-hour Duration Rainfall Depth)


2-yr 4.77 5.0 -4.6% 5.0 -4.6%lO-yr 8.28 8.2 1.0% 8.5 -2.6%50-yr 11.71 10.0 17.1% 11.0 6.5%100-yr 13.16 12.5 5.3% 13.0 1.2%


From the results based on both the Gumbel distribution and the Log Pearson Type

III distribution, we can see that most of the new results on rainfall frequency at selected

sites on Oahu are close to the results reported in R-73 (1984), but show slightly larger

differences from the results in TP-43 (1962). Some of the larger differences are mostly

41

due to the fact that the results in the previous reports were presented in a "map" style, i.e.,

constant-value curves drawn over a rough outline of the Oahu bathymetry. As a result,

the rainfall frequency values are difficult to read accurately for some locations from these

curves.

We also note that for rainfall frequency analysis, the Gumbel Distribution gives a

slightly better prediction in long return frequency (i.e. 100-year storm) than the Log

Pearson Type ill Distribution. Table 2.20 summaries the results taken from Table 2.7-

2.12 and Table 2.14-2.19. The difference comparison is based on the Gumbel results.

This confirms the similar finding from R-73 (1984).

Table 2.20 Comparison between Gumbel Distribution and Log Pearson Type III Distribution in

Predicting lOO·Year, 24-Hour Storm

Storm Specification: Frequency =100 years, Duration =24 hours, Unit =InchesStation Gumbel Log Pearson Type ill Difference

Hawaii Kai Golf Course 724.19 10.26 10.26 0.0%Kahuku 912 12.64 13.2 -4.4%

Kailua Fire Station 791.3 9.76 8.54 12.5%Makaha 10.28 8.65 15.9%

Pupukea Heights 896.4 10.94 9.69 11.4%Waimea 892 13.44 13.16 2.1%

2.4 Annual Series and Partial Series

In the previous sections of rainfall frequency analysis, only one extreme value per

year is used, and thus the result is defined as an annual series. However, it is often

observed that the top greatest events in one year exceed the annual extremes in some

other years. The analysis of extreme values without considering the annual occurrence is

defined as a partial series. It is clear that the annual series will not catch all the greatest

42

events of the records, and the use of partial series provides more accurate representation

of the actual data in reality. However, there is no theoretical basis on the relationship

between the two series, and conventional converting equation is not available. In order to

convert the annual series into partial series, a derived empirical factor is recommended.

Langbein (1949) has shown the two series are highly related and approach each other in

the long-term periods. Table 2.21 provides the empirical factor values for return intervals

up to 10 years. It is similar to Table 2 in TP-43 and is derived from 50 widely scattered

stations in the United States. Chow (1964) indicated that there is no adjustment required

for return intervals greater than 10 years since both series tend to approach each other

after 10 years.

Table 2.21 Empirical Factors for Converting Annual Series to Partial Series

Return Interval Annual Series Partial Series

2-year 1 1.136

5-year 1 1.042

lO-year 1 1.010

For this study, the annual extremes are first used to form an annual series. After

the frequency analysis, the results are multiplied by the empirical factors for return

intervals less or equal to 10 years.

2.5 Intensity-Duration-Frequency Curves

As mentioned in chapter 1, one of the runoff models, i.e., the rational method, will

be examined in this study for its accuracy in predicting peak discharge in a selected

43

gaged watershed on Oahu. One of the key parameters in the rational method is rainfall

intensity in inches per hour for a design storm with duration equal to the time of

concentration. Depending on the return interval T and the time of concentration, rainfall

intensity will vary from case to case. Usually the value of rainfall intensity is obtained

from the so-called Intensity-Duration-Frequency (IDF) curves. Given the time of

concentration and return interval, rainfall intensity can be interpolated from the curves.

To produce equilibrium peak discharge, it is suggested that a locally derived IDF curve

shall be used in the design process. Thus, this section will present the methodology and

results of constructing IDF curves based on 15-minute precipitation records for rain gage

stations Kailua Fire Station 791.3 and Waimea 892.

The 15-minute format raw data are obtained from the NCDC website for both rain

gage stations. Data for Kailua Fire Station 791.3 are from 1977 to 2001, and data for

Waimea 892 are from 1978 to April 2002. The gages, which are autographic gages, take

values in every 15-minute interval starting from the midnight of a calendar day. Thus the

values can be considered as true-interval value in this section, and no conversion is

required. However, only when rainfall amount is significant such as during a storm, the

detected precipitation values will be recorded. Some small values, which are usually less

than tenths of an inch, are neglected and not shown on the records. The way it obtains the

precipitation values will produce discontinuity in the data itself. This discontinuity may

cause some problems when the data are processed.

The first problem is that for a long rain duration such as I-hour or longer, rainfall

intensity may not be found because of the discontinuity. A typical example taken from

Kailua Fire Station 791.3 can illustrate the idea. In the year 1998, no storm duration

44

longer than 105 minutes can be found, and this indicates that a zero value of rain intensity

will be used in the statistical analysis, which will produce inaccurate results. The second

observed problem is called "missing duration". For example, a storm may start to rain for

some periods of times, but stop raining for a short time all of a sudden, and then continue

to rain again. During the no-rain period, the actual rainfall amounts might be too small to

be recognized by the rain gage. Thus it is assumed that there is no rain record for that

particular period. The "missing duration" is here defined as the "no-rain situation" period

as mentioned above. The approach used to solve the problems in this study is to add more

15-minute intervals containing zero precipitation values to make it a continuous record.

To illustrate the idea, an example of storm record in Table 2.22 and Table 2.23 are

prepared for the purpose of better understanding, and the method is applied throughout

the analysis for all data sets.

Table 2.22 Sample Data before Adding More IS-Minute Intervals

Time IntervalPrecipitation per Precipitation per Precipitation per

15-min interval (in) 45-min interval (in) 120-min interval (in)

7:45 (7:31-7:45) 0.1 0.0 0.0

8:00 (7:46-8:00) 0.1 0.0 0.0

8:15 (8:01-8:15) 0.5 0.7 (7:45 - 8:15) 0.0

8:30 (8: 16-8:30) 0.4 1.0 (8:00 - 8:30) 0.0

9:00 (8:46-9:00) 0.6 (8:30 - 9:00) 0.0

9:15 (9:01-9:15) 0.5 0.0

45

Table 2.23 Sample Data after Adding More IS-Minute Intervals

Time IntervalPrecipitation per Precipitation per Precipitation per

15-min interval (in) 45-min interval (in) 120-min interval (in)

7:45 (7:31-7:45) 0.1 0.0 0.0

8:00 (7:46-8:00) 0.1 0.0 0.0

8:15 (8:01-8:15) 0.5 0.7 (7:45 - 8: 15) 0.0

8:30 (8:16-8:30) 0.4 1.0 (8:00 - 8:30) 0.0

8:45 (8:31-8:45) 0.0 0.9 (8: 15 - 8:45) 0.0

9:00 (8:46-9:00) 0.6 1.0 (8:30 - 9:00) 0.0

9:15 (9:01-9:15) 0.5 (8:45 - 9: 15) 0.0

9:30 (9: 16-9:30) 0.0 1.1 (9:00 - 9:30) (7:45 - 9:30)

For 45-minute and 120-minute durations, Table 2.23 gives values of 1.1 inches

and 2.2 inches respectively, where Table 2.22 gives 1 inch for 45-minute duration and

zero accumulated amount for 120-minute duration. It is clearly shown that by making the

data set as complete as it should be, the end results will be more realistic and reliable.

In order to better illustrate how IDF curves are constructed, a sample record taken

from Kailua Fire Station 791.3, Table 2.24, containing 15-minute rainfall duration is

provided with step-by-step explanation. This sample is to determine the relationship

between rainfall intensity of 15-minute duration and return intervals up to 25 years (n =

25 years). First, annual maximum value for each year is picked and converted to hourly

basis, and then sorted in descending order. Ranks are given to each values. Notice that

there are repeated numbers of same rainfall intensity, which will cause problems for

short-term records when calculating return interval. In order to eliminate the associated

problems, the USGS mean order method is proposed. Table 2.25 is prepared to illustrate

the idea.

46

Table 2.24 Maximum I5-Minute Duration Rainfall For Kailua Fire Station 791.3

Annual Series, Maximum IS-Minute Duration Rainfall

Column 1 Column 2 Column 3 Column 4 Column 5 Column 6

Rain Rain Rain RainYear Rank

(in/15rnin) (in/hr) (in/15rnin) (in/hr)

1977 1 4 1 1.6 6.4

1978 0.5 2 2 1.2 4.8

1979 0.7 2.8 3 1.2 4.8

1980 0.7 2.8 4 1.1 4.4

1981 0.5 2.0 5 1 4

1982 1.2 4.8 6 1 4

1983 0.3 1.2 7 0.9 3.6

1984 0.7 2.8 8 0.9 3.6

1985 1.6 6.4 9 0.8 3.2

1986 0.8 3.2 10 0.8 3.2

1987 1 4 11 0.8 3.2

1988 0.6 2.4 12 0.8 3.2

1989 0.8 3.2 13 0.7 2.8

1990 0.4 1.6 14 0.7 2.8

1991 0.9 3.6 15 0.7 2.8

1992 1.2 4.8 16 0.7 2.8

1993 0.4 1.6 17 0.6 2.4

1994 0.4 1.6 18 0.5 2

1995 0.8 3.2 19 0.5 2

1996 0.8 3.2 20 0.4 1.6

1997 1.1 4.4 21 0.4 1.6

1998 0.2 0.8 22 0.4 1.6

1999 0.4 1.6 23 0.4 1.6

2000 0.7 2.8 24 0.3 1.2

2001 0.9 3.6 25 0.2 0.8

47

Table 2.25 USGS Mean Order Method

Annual Series, Maximum 15-Minute Duration Rainfall

Column Column Column Column Column Column Column

1 2 3 4 5 6 7

Mean

Rainfall Frequency Cumulative Rank Order CDF T

(in/hr) Frequency Order =m = m/(n+l) = lI(1-CDF)

0.8 1 1 1 1 0.0385 1.04

1.2 1 2 2 2 0.0769 1.08

1.6 4 6 3-6 4.5 0.1731 1.21

2 2 8 7-8 7.5 0.2885 1.41

2.4 1 9 9 9 0.3462 1.53

2.8 4 13 10-13 11.5 0.4423 1.79

3.2 4 17 14-17 15.5 0.5962 2.48

3.6 2 19 18-19 18.5 0.7115 3.47

4 2 21 20-21 21.5 0.8269 5.78

4.4 1 22 22 22 0.8462 6.50

4.8 2 24 23-24 23.5 0.9038 10.40

6.4 1 25 25 25 0.9615 26.00

As mentioned in the previous paragraph, the USGS mean order method is applied

here to determine return intervals for specific rainfall duration. Values in column 1 of

Table 2.25 are taken from Column 6 of Table 2.24 and ranked in ascending order.

Column 2 and 3 are frequency and cumulative frequency observed for each rainfall

intensity of Column 1 during the recording period n, which is 25 years in this case. Rank

orders are given in Column 4 according to the cumulative frequency, and each cell in

Column 5 is the average value of Column 4. For instance, for maximum rainfall intensity

equaling 2 in/hr, there are four occurrences in the 25-year period (n=25) indicating the48

frequency should be input as four in Column 2. And cumulative frequency is just the

summation of frequency values, and it should be input as six in this example. Rank orders

3-6 (three to six) are given in Column 4 since the first two rank orders are occupied

already. Column 5, given a symbol as "m", is easily obtained by simply taking average of

Column 4, which is 4.5 in this case. Column 6, Cumulative Density Function (CDF) is

equal to rn/(n+1). The final step is to determine return interval, T, which is equal to 1/(1

CDF) in Column 7. The same procedures are repeated for other cells to complete Table

2.24. This completes one full analysis for rainfall duration of 15 minutes.

The analyses for 30-, 45-, 60-, 75-, 90-, 105-, 120-, 180-, and 240-minute duration

are also performed following the same steps. Since there are 25 years of data available,

five return intervals, 5-, 10-, 15-, 20-, and 25-year are chosen as target return intervals in

the IDF curves for the USGS mean order method. Best fitting curves and linear

interpolation are applied if necessary when determining rainfall intensity under certain

return intervals. For example, to determine rainfall intensity of 15-minute duration under

the five target return intervals, best fitting curve is constructed using Column 1 and 7

from Table 2.25 to obtain the desired values for 15-minute rain duration case.

The above sample used the USGS mean order method to construct IDF curves for

rain gage station Kailua Fire Station 791.3. Since both Gumbel Distribution and Log

Pearson Type ill Distribution were examined in the previous section, they are also

applied to construct IDF curves in this section. The procedures used here are exactly the

same as described in the previous sections. For rain gage station Waimea 892, all three

methods (namely, the USGS mean order, Gumbel, and Log Pearson Type ill) are applied.

Table 2.26 and 2.27 summarize the results, and the IDF curves for both rain gage stations

49

are presented in Figures 2.14 - 2.19. To distinguish from the two distributions, the USGS

mean order method is denoted as field data in the summary and figures.

50

Table 2.26 IDF Curves Summary, Waimea 892

Gumbel I Unit =Inches I2-yr 5-yr lO-yr 15-yr 20-yr 25-yr 50-yr 100-yr

15-min 2.31 3.24 3.86 4.21 4.45 4.64 5.22 5.7930-min 1.87 2.68 3.21 3.52 3.73 3.89 4.39 4.8945-min 1.60 2.32 2.80 3.06 3.25 3.40 3.84 4.2860-min 1.43 2.10 2.55 2.80 2.98 3.11 3.53 3.9875-min 1.27 1.89 2.29 2.52 2.68 2.80 3.18 3.5690-min 1.15 1.75 2.15 2.37 2.53 2.65 3.03 3.40105-min 1.04 1.64 2.03 2.25 2.41 2.53 2.90 3.26120-min 0.97 1.54 1.92 2.14 2.29 2.41 2.76 3.12180-min 0.78 1.23 1.53 1.70 1.82 1.91 2.19 2.46240-min 0.63 1.01 1.26 1.40 1.50 1.57 1.80 2.04

lLo2 Pearson Type III I Unit = Inches I2-yr 5-yr lO-yr 15-yr 20-yr 25-yr 50-yr 100-yr

15-min 2.39 3.23 3.67 - - 4.18 4.49 4.7630-min 1.93 2.69 3.10 - - 3.53 3.79 4.0245-min 1.64 2.31 2.69 - - 3.11 3.37 3.6060-min 1.44 2.08 2.46 - - 2.90 3.19 3.4675-min 1.28 1.85 2.21 - - 2.62 2.90 3.1790-min 1.13 1.69 2.06 - - 2.51 2.84 3.15105-min 1.02 1.57 1.94 - - 2.42 2.77 3.12120-min 0.93 1.46 1.83 - - 2.31 2.68 3.06180-min 0.76 1.17 1.46 - - 1.84 2.13 2.42240-min 0.61 0.96 1.20 - - 1.52 1.76 2.00

~ield Data I Unit =Inches I2-yr 5-yr lO-yr 15-yr 20-yr 25-yr 50-yr 100-yr

15-min - 3.42 3.79 3.94 4.05 4.13 - -30-min - 2.81 3.11 3.24 3.33 3.39 - -45-min - 2.42 2.77 2.84 2.88 2.92 - -60-min - 2.19 2.53 2.65 2.73 2.79 - -75-min - 1.87 2.28 2.45 2.55 2.63 - -90-min - 1.72 2.11 2.34 2.51 2.64 - -105-min - 1.64 2.05 2.24 2.38 2.49 - -120-min - 1.50 2.02 2.21 2.31 2.39 - -180-min - 1.20 1.55 1.75 1.84 1.89 - -240-min - 0.96 1.30 1.48 1.49 1.50 - -

51

Table 2.27 IDF Curves Summary, Kailua Fire Station 791.3

Gumbel I Unit =Inches I2-yr 5-yr lO-yr 15-yr 20-yr 25-yr 50-yr 100-yr

15-min 2.78 4.14 5.04 5.55 5.91 6.18 7.03 7.8630-min 2.16 3.41 4.23 4.69 5.02 5.27 6.04 6.8145-min 1.78 2.81 3.50 3.89 4.16 4.37 5.01 5.6560-min 1.56 2.47 3.06 3.40 3.65 3.82 4.38 4.9375-min 1.37 2.13 2.63 2.92 3.12 3.27 3.74 4.2190-min 1.23 1.92 2.38 2.63 2.81 2.95 3.38 3.80105-min 1.13 1.76 2.18 2.42 2.59 2.71 3.11 3.50120-min 1.05 1.64 2.03 2.26 2.41 2.53 2.90 3.26180-min 0.79 1.23 1.51 1.68 1.79 1.88 2.15 2.42240-min 0.65 1.01 1.24 1.38 1.47 1.55 1.77 1.99

Lo~ Pearson Type III I Unit =Inches I2-yr 5-yr lO-yr 15-yr 20-yr 25-yr 50-yr 100-yr

15-min 2.82 4.07 4.81 - - 5.63 6.18 6.6830-min 2.13 3.24 3.97 - - 4.88 5.54 6.1845-min 1.75 2.70 3.31 - - 4.06 4.59 5.1160-min 1.55 2.39 2.91 - - 3.53 3.97 4.3775-min 1.37 2.08 2.53 - - 3.05 3.41 3.7490-min 1.23 1.89 2.29 - - 2.75 3.05 3.33105-min 1.12 1.73 2.11 - - 2.54 2.83 3.10120-min 1.05 1.61 1.96 - - 2.35 2.60 2.84180-min 0.79 1.21 1.46 - - 1.74 1.93 2.09240-min 0.66 1.00 1.20 - - 1.41 1.54 1.66

!Field Data I Unit =Inches I2-yr 5-yr lO-yr 15-yr 20-yr 25-yr 50-yr 100-yr

15-min - 4.00 4.80 5.33 5.79 6.35 - -30-min - 3.22 4.28 4.77 5.13 5.46 - -45-min - 2.62 3.85 4.07 4.19 4.28 - -60-min - 2.34 3.25 3.47 3.60 3.69 - -75-min - 2.22 2.64 2.83 2.98 3.10 - -90-min - 2.06 2.38 2.51 2.59 2.66 - -

105-min - 1.89 2.11 2.36 2.40 2.45 - -120-min - 1.77 1.97 2.10 2.21 2.33 - -180-min - 1.28 1.41 1.50 1.67 1.83 - -240-min - 1.00 1.22 1.34 1.42 1.49 - -

52

IDF Curves for Waimea 892 (Gumbel)

!--IOOyears --50years -- 25 years --20years 15years - 10years -- Syears --2years I

240225210195180165ISO13S120lOS907S60453015

1

0.5

o I ,

o

6

5.5

5-i 4.5_ 4

.~ 3.5;i 3

= 2S

t~VI~

Time ofConcentntion (minutes)

Flpre 2.1S IOF Curves, Gumbel Distribution, Waimea m

IDF Cwves for Waimea 892 (Log Peanon Type 111)

1-- 100 years -- 50 years - 25 years -- 10 years -- 5 years -- 2 years I5

4.5

4'l:':I 3.5-~ 3•t:l.a 25!

VI = 2VI .a! 1.5

1

0.5

0

0 15 30 45 60 75 90 105 120 135 150 165 180 195 210 225 240

Time ofConuntntion (miDutel)

Figure 2.16 IDF Curves, Log Pearson Type Ill, Waimea 892

IDF Cmves for Kallua Fire Station 791.3 (Field Data)

!--25 years --20years 15years --lOyears --5years I

","'"-~'"~ -,~

"'-. ~-" -~.

~ ,,~,

~ ~~,

"--- ",,-~-- ----~---~ - ~

,

6.5

6

5.5

'i:' 5

] 4.5-.to ....; 3.5.a.:l 3

~ i 25.s 2

&! 1.5

1

0.5

oo 15 30 45 60 75 90 105 120 135 150 165 180 195 210 225 240

Time of Concentration (minutes)

Figure 2.17 IDF Curves, USGS Mean Order Method, Kailua fire Station 791.3

From the above presentations, we can see that producing IDF curves not only

requires data of high resolution but it is also a very time consuming task. For engineering

applications, sometimes a simple empirical correction factor is used in converting the 1-

hour rainfall intensity to intensities of other durations. In the Rules Related to Storm

Drainage Standards (2000) published by the City and County of Honolulu, the correction

factor is plotted in Plate 4. It is used to convert I-hour rainfall intensity to rainfall

intensity of various durations for application of the rational method. In this study, IDF

curves are derived for Kailua Fire Station 791.3 and Waimea 892. They will be used to

examine the validity of the correction factor values in Plate 4. The correction factor is

defined in terms of a ratio. It is assumed that the rainfall duration of 60 minutes

corresponds to the correction factor of 1. All calculations of correction factor for various

rainfall durations are based on the comparison with 60-minute rainfall duration. The

equation is given as follows:

ICF =_1

1 160

where

CFt =Correction Factor corresponding to rainfall duration of 1 minutes

It =rainfall intensity corresponding to rainfall duration of 1 minutes

160 =rainfall intensity corresponding to rainfall duration of 60 minutes

The rainfall intensity for specific rainfall duration and return interval can be read

from Table 2.28 and 2.29, and summary tables are prepared. A figure similar to Plate 4 is

also provided as a comparison.

59

Table 2.28 Correction Factor, Waimea 892

Waimea892 I Plate 4 ITc Factor Tc Factor Tc Factor

15-min 1.90 75-min 0.85 180-min 0.5030-min 1.40 90-min 0.7845-min 1.20 105-min 0.7060-mini 1.00 120-min 0.65

Factor: Gumbel DistributionTc 5-year lO-year 25-year 50-year 100-year Average

15-min 1.54 1.51 1.49 1.48 1.45 1.5030-min 1.27 1.26 1.25 1.24 1.23 1.2545-min 1.10 1.10 1.09 1.09 1.08 1.0960-min 1.00 1.00 1.00 1.00 1.00 1.0075-min 0.90 0.90 0.90 0.90 0.89 0.9090-min 0.83 0.84 0.85 0.86 0.85 0.85105-min 0.78 0.80 0.81 0.82 0.82 0.81120-min 0.73 0.75 0.77 0.78 0.78 0.77180-min 0.62 0.60 0.61 0.62 0.62 0.61240-min 0.48 0.49 0.50 0.51 0.51 0.50

Factor: L02 Pearson Type III DistributionTc 5-year lO-year 25-year 50-year 100-year Average


Factor: USGS Mean Order Method (Field Data)Tc 5-year lO-year 15-year 20-year 25-year Average


60

Table 2.29 Correction Factor, Kailua Fire Station 791.3

Kailua Fire Station 791.3 I Plate 4 ITc Factor Tc Factor Tc Factor

IS-min 1.90 75-min 0.85 180-min 0.5030-min 1.40 90-min 0.7845-min 1.20 lOS-min 0.7060-mini 1.00 l20-min 0.65

Factor: Gumbel DistributionTc 5-year lO-year 25-year 50-year 100-year Average

IS-min 1.68 1.65 1.62 1.60 1.59 1.6330-min 1.38 1.38 1.38 1.38 1.38 1.3845-min 1.14 1.14 1.14 1.14 1.14 1.1460-min 1.00 1.00 1.00 1.00 1.00 1.0075-min 0.86 0.86 0.85 0.85 0.85 0.8690-min 0.78 0.78 0.77 0.77 0.77 0.77lOS-min 0.71 0.71 0.71 0.71 0.71 0.71l20-min 0.67 0.66 0.66 0.66 0.66 0.66180-min 0.50 0.49 0.49 0.35 0.49 0.46240-min 0.41 0.41 0.40 0.40 0.40 0.40

Factor: Lo~ Pearson Type III DistributionTc 5-year lO-year 25-year 50-year 100-year Average


Factor: USGS Mean Order Method (Field Data)Tc 5-year lO-year IS-year 20-year 25-year Average


61

I I , I

I I

I

==---- - '.

--.0;.

...... --- I

I ~ --I I ~ -- !

I I --- I

I

I

I.'--

0\N

i~

1~

10

0.1

10

COJTection Factor

--Plate 4 --Waimea 892 --Kailua Fire Statioon 791.3 I

100

Duration ofRainfaU InteDSity (Min)

Figare 2.20 Correction Factor Plot

1000

These results show that the correction factor depends on return period and it

varies from location to location. Compared with the values for the correction factor given

in the drainage standard, the present result gives a smaller value for short duration and a

greater value for longer durations. However, the differences are not significant and are

within acceptable ranges (0 - 30%) for engineering applications. If sufficient research

resources are available, it will be better if IDF curves for more watersheds in Hawaii are

determined for more accurate predictions of rainfall intensity for different durations.

2.6. Effect of Record Length on Accuracy of Prediction

In engineering designs, for example, in the design of bridges in floodplains, the

design flood is usually the 100-year flood. However, most of the rain-gage and stream

gage records are shorter than 100 years. This is the reason that certain probability

distributions, such as the Gumbel or the Log Pearson Type III distributions, have been

developed for prediction of rainfall or stream flow frequency. The idea is that if these

distributions based on the records of relatively short periods (say 25 years) appear as

straight lines in a graph with the appropriate coordinate scales, then these lines can be

linearly extended to predict the rainfall or stream flow for a longer return period (say 100

years). In this study, we will examine the effect of rainfall record length on the accuracy

of predicting rainfall frequency in Hawaii based on the Gumbel distribution. Two rain

gage stations, Waimea 892 and Kahuku 912 on Oahu, are chosen for this study. The

reason these two stations are selected is that both have relatively long records: station

Waimea 892 contains rainfall records of 84 years from 1919 to 2002 and station Kahuku

63

912 has records of 82 years from 1919 to 2001, excluding year 1975. These long records

provide us with a good database for the verification study of our interest. The specific

steps and objectives for this study are explained in the following paragraphs.

First, the annual extreme daily rainfall depth of return period 80 years is obtained

based on the actual rainfall data for the two stations through statistical analysis of the full

data record. The numbers calculated in this manner are considered as the actual 80-year

rainfall depth. To examine the effect of record length on the accuracy of rainfall

frequency prediction based on the Gumbel distribution, for each station, we prepare

randomly generated IS-year, 20-year, 30-year and 40-year records from the full record of

the actual rainfall data recorded at the station. Forty sets of records are generated for each

record length for each station. In generating these shorter records, two methods are used.

These methods will be explained by using Waimea 892 Station and the length of 20 years

as an example. The first method is to let a computer randomly choose 20 values from

Waimea's 84 data points. These twenty values will form one set of rainfall record of

twenty years for Waimea. This is repeated 20 times and therefore twenty randomly

generated rainfall records of 20 years are obtained. The second method is to let the

computer randomly select a year from all the years in the full record, and the rainfall data

for this year along with the continuous record of 19 years following the selected year will

form a set of rainfall record of 20 years. This is also repeated 20 times to create 20 sets of

record in this manner. Combining the results from both methods, we obtain forty

randomly generated rainfall records of twenty years from the original full record. After

that, Gumbel distribution based on each twenty-year record is determined and the

64

predicted 80-year rainfall depth from the Gumbel distribution is obtained. The predicted

value is then compared with the actual value to examine the accuracy of the prediction.

The following table summarizes the results of 40 trials for both stations.

Table 2.30 Comparison between the Actual and Predicted 80-year Rainfall for Waimea 892 RainGage and Kahuku 912 Rain Gage Stations

Waimea 892 Rain Gage Station15-year data 20-year data 30-year data 40-year data

Maximum50% 38% 31% 26%

differenceMinimum

0.0% 0.6% 1.6% 0.1%differenceAverage

18% 15% 11% 8.6%DifferenceProbability ofdifference

0.29 0.17 0.05 0.02being greaterthan 25%Probability ofdifference

0.02being greater - - -

than 50%Kahuku 912 Rain Gage Station

Maximum70% 51% 48% 36%

differenceMinimum

1.0% 1.0% 0.8% 2.2%differenceAverage

21% 21% 18% 14%DifferenceProbability ofdifference

0.39 0.41 0.20 0.05being greaterthan 25%Probability ofdifference

0.12 0.05 0.02being greater

-

than 50%

65

More detailed results for the forty trials for each station can be found in Tables

Al and A2 in the Appendix A. These results show that as the record length increases, the

error in the prediction will decrease. This is an expected result. Examining the

quantitative results, we note that the average error in the predictions based on all the

records is quite modest and similar, as it ranges from 8.6% to 21 %. The chances to have

an error more than half of the true value is very small even when the prediction is based

on a short IS-year record. This indicates that for rough engineering estimates, 15 to 20

year records are sufficient for predicting an 80-year rainfall by applying the Gumbel

distribution. However, for more accurate and reliable predictions, 30- to 40-year records

are more preferable. The results are solely based on the two rain gage stations. To have

more generalized conclusion, more stations should be chosen from each micro-climate

watershed, and more trials should be performed to ensure the completeness of sensitivity

analysis for the entire Oahu Island.

66

CHAPTER 3. COMPARISON AMONG THREE DIFFERENT METHODS FOR

PREDICTION OF STREAM DISCHARGE

Predicting stream discharge under different flood conditions is of great

importance in engineering design of bridges, culverts and other structures. If the stream is

gauged and has sufficiently long stream flow record, then discharge values for different

return frequency can be calculated through statistical analysis of the stream record

directly. In reality, many streams are un-gauged. In this case, a mathematical model that

links rainfall intensity and stream flow is needed. Currently, there are three different

methods for predicting stream flow based on rainfall information. They are Soil

Conservation Service's TR-20 method, the USGS regression method, and the rational

methods. All three methods are highly empirical and involve at least one or more

empirical coefficients in the equations. The methods must be validated for each region or

local watershed.

The objective of the current study is to examine the validity, accuracy and

efficiency of the three methods for predicting stream discharge for watersheds on Oahu.

This is done by applying the three methods to predict stream flow and comparing the

predicted values with the recorded values. Waimea Watershed, which is gauged and has

both rainfall and stream flow records, is selected as a case study.

3.1 Description of Waimea Watershed and Kamananui Stream

Waimea Watershed is located on the northwestern part of the Oahu Island (Figure

3.1). Topographic characteristics are dominated by the mountainous area, i.e., the Koolau

67

Range. There are only a few residential areas in the watershed and they are located near

the coast. Most of the landscape within the watershed can be seen as forest type. The

main drainage channel within the watershed is called the Kamananui Stream. It originates

from the Koolau Range and runs westward into the Pacific Ocean. Both rain gage

(Waimea 892) and stream gage (Station 330000) are identified at the downstream end of

the stream near the coastal area.

Waimea Watershed

Figure 3.1 Waimea Watershed on Oahu

3.2 Commonly Used Methods for Predicting Stream Flow

3.2.1 Soil Conservation Service Technical Release-20 (TR-20)

One of the methods for stream flow prediction was developed by the U.S. Soil

68

Conservation Service (SCS), now known as the Natural Resources Conservation Service

(NRCS). The method is entitled Technical Release-20 (TR-20). It is used by hydraulic

engineers for estimating runoff volume and peak discharge for urban areas. TR-20 is a

computer program written in FORTRAN and is designed to be an engineering-oriented

package. The program reads input data sheet, which contains parameters prepared by the

user, and determines runoff hydrographs for the design storms. After reading in the

provided information, the program will develop flood hydrograph and routes it through

reservoir and stream channel if required. Hydrographs are combined with others from

tributaries at outlet point of the drainage area to obtain the final runoff. Flow diversion

and base flow functions are also provided as optional tools. Typical computation

sequence is illustrated in Figure 3.2 and summarized below.

Outlet (point of concentration)

Figure 3.2 TR-20 Computation Sequence

The watershed is divided to several subbasins, which are labeled as A, B, C, D,

69

and E in Figure 3.4. R denotes a reservoir. First of all, hydrographs are computed for

subbasins A and B and then combined as one single hydrograph and routed to the

upstream end of reservoir R. It is later combined with hydrographs generated by

subbasins C and D and routed through reservoir R. The hydrograph at the downstream

end of reservoir R will be routed to outlet point and combined with hydrograph generated

by subbasin E. Channel routing is only performed between the outlet point and the

downstream end of reservoir in this example.

In order to run the TR-20 computer program, several parameters of the watershed

such as watershed characteristics, stream cross-section, structure data, and storm data

must first be identified as input parameters to perform the analysis. For this thesis study,

the watershed is simplified assuming reservoir and channel routings are insignificant. The

required parameters in this study for TR-20 include runoff Curve Number (CN), 24-hour

rainfall depth amounts of design storm at specified return frequency, drainage area, time

of concentration (Tc), antecedent moisture condition, and rainfall distribution type.

The runoff Curve Number (CN) is a parameter that takes care of the combined

effects of soil types, land use, vegetative cover, and infiltration situation within the

watershed. A Curve Number table has been developed by SCS to represent various

conditions of a watershed. In order to use the table, land use description and hydrologic

soil groups of the watershed must be found. Land use description of particular areas can

be obtained from local government publications and/or from the developers' conceptual

plan. SCS publishes a report entitled "Erosion and Sediment Control, Guide for Hawaii"

containing a table that provides a list of most hydrologic soils in the United States and

70

their group classifications. Hydrologic soil groups, as defined by SCS soil scientists, are

indicators to take account the effect of infiltration rate. Infiltration rates of soils vary

widely from case to case, and depending on the soil types, runoff amount will be

significantly affected. Hydrologic soil groups are defined in four categories: A (low

runoff potential), B (moderately low runoff potential), C (moderately high runoff

potential), and D (high runoff potential). By obtaining both land use and hydrologic soil

type, the runoff Curve Number can be extracted from a report entitled "Urban Hydrology

for Small Watersheds, TR-55" according to antecedent moisture conditions and the types

of cover. There are three types of antecedent moisture conditions: AMC I, AMC II, and

AMC III. The conditions AMC I and AMC III denote the extreme dry and wet soils,

respectively, while AMC II denotes the average case. The runoff Curve Number obtained

from the report applies to AMC II condition only, but with specification in the input

sheet, TR-20 program will make adjustment for AMC I and AMC III conditions. One

important issue to notice here is that a watershed usually contains various soil types and

land use conditions. Therefore, a composite runoff Curve Number must be used by

weighting each Curve Number according to its area.

Another input parameter required for TR-20 is the rainfall amounts received by

the watershed, and it is expressed in term of depth (inches). The duration of the design

storm here is specified as the 24-hour period. The information of rainfall can be found

from statistical analysis of rainfall records or from existing reports either the "Rainfall

Frequency Study for Oahu, Report R-73, 1984" or the "Rainfall-Frequency Atlas of

Hawaiian Island, Technical Paper No. 43, 1962". For the selected Waimea Watershed,

71

frequency analysis based on NOAA rain gages Waimea Station 892 is performed to

obtain the 24-hour rainfall depths as described in the previous chapter. The 24-hour

rainfall depth varies with return frequency as well as geographic locations. Figure 3.3

taken from "Urban Hydrology for Small Watersheds, TR-55" represents various regions

of the United States. As indicated in the report, Type I and IA represent the Pacific

maritime climate. Type III represents Gulf of Mexico and Atlantic coastal areas. Type IT

represents the rest of the country. TR-20 program will make necessary adjustment

according to specification of rainfall distribution in the input sheet.

",,- ..

Typ •

....,,'"~'" Typ. IA

DTyp. II

TyP' I II

C=?... oJ'

""

Figure 3.3 Geographic Boundaries for SCS Rainfall Distributions

Information about the size of the drainage area of Waimea Watershed can be

found using the GIS software package. The required layer information can be

72

downloaded either from Hawaii Statewide GIS program or City and County of Honolulu

Department of Planning and Permitting websites.

The last parameter required is time of concentration, Tc. Time of concentration is

the time it takes water to travel from the hydraulically most distant point of the watershed

to the point of interest within the watershed. Time of concentration is the sum of travel

time T t values for various consecutive flow segments. The following procedures are

suggested to calculate time of concentration in SCS TR-55 manual: sheet flow (SF),

shallow concentrated flow (SCF), and open channel flow (OCF).

Sheet flow usually occurs in the starting point of streams (headwater). With sheet

flow, Manning's roughness coefficient plays an important role to account for geologic

effects. Manning's kinematic solution is used to compute T t for sheet flow of less than or

equal to 300 feet.

T = 0.007(nL)0.8t ( P

z)0.5 S 0.4

where:

Tt = travel time (hour)

n =Manning's roughness coefficient (TR-55 manual Chapter 3)

L = flow length (ft)

Pz =2-year, 24-hour rainfall depth (in)

s =land slope (ft/ft)

(3.1)

After 300 feet of travel distance, sheet flow usually becomes shallow concentrated

flow. To calculate travel time, average velocity of shallow concentrated flow must be

determined. Figure 3.4 taken from the TR-55 manual displays that the average velocity is

73

the function of land slope and channel type. After obtaining average velocity, travel time

can be estimated by dividing flow length with average velocity from equation (3.2). For

those locations where land slope is less than 0.005 ft/ft, equation (3.3) for unpaved

condition and equation (3.4) for paved condition can be used to estimate the travel time

for shallow concentrated flow.

where:

Tt =travel time (hour)

L =flow length (ft)

v=average velocity (fUsee)

s = land slope (fUft)

T = Lt 3600*V

v =16.1345 *(s)o.s

v =20.3282 *(s)O.5

(3.2)

(3.3)

(3.4)

As stated in the TR-55 manual, it is suggested that open channel flows are

assumed to begin where channels are visible on aerial photo or where blue lines

(indicating stream) appear on USGS quadrangle sheets. Manning's equation is normally

applied to calculate the average flow velocity for open channel flows (equation (3.5)). If

open channel is observed, it is suggested that a channel routing should be also considered

in the TR-20 model. Cross-sectional information of the open channel section of the

stream should be obtained from the field by topographic survey. Equation (3.2) is

applicable to estimating travel time for open channel flows if the average flow velocity is

74

known.

1 49 2/3 1/2V = . r s

n

where:

V = average velocity (ft/sec)

r =hydraulic radius (ft)

s =channel slope (ft/ft)

n =Manning's roughness coefficient for open channel flow

(3.5)

After the necessary parameters are obtained, as described in "Technical Release

No. 20, Computer Program for Project Formulation Hydrology", an input text file

containing watershed information such as composite curve number, rainfall depth,

drainage area, and time of concentration, etc. should be prepared in order to run the TR-

20 program. A sample input file TR-20 run is provided in the Appendix B for better

understanding. For detailed information about the input file format, refer to TR-20

manual. After executing the program, a summary report will be generated automatically

for the design storm. Peak runoff of the watershed can then be obtained. Special attention

must be paid to the format of the input text file. Since TR-20 is written in FORTRAN,

specific columns in the file are designed to carry out specific commands. Manning's

roughness coefficient for open channel flow can be obtained from standard textbooks

such as Chow (1959).

75

.50-••1

.20 -

+..> .10..... -.......+>.....

..QJ

.060. -0-lI'IQJlI'I .04So. -::::J0<)So.G.I+>IllS:3

.02 -

.005 - ..1-I.L....~.I.""J~I...l..I...I.L.,I""l",ju.l..............1~1.w.1~I~I-...............~I

1 2 4 6 10 20Average velocity, ft/sec

Figure 3.4 Average Velocity for Shallow Concentrated Flow

76

3.2.2 United States Geological Survey (USGS) Regression Method

The second method for predicting peak discharge is called the United States

Geological Survey (USGS) Regression Method. In 1993, the USGS and Federal Highway

Administration decided to compile a computer program called "The National Flood

Frequency (NFF) Program" utilizing regression equations for most states. For the island

of Oahu, the regression equations were developed by Wong (1994) with cooperation

from the City and County of Honolulu. A report, titled "Estimation of Magnitude and

Frequency of Floods for Streams on the Island of Oahu, Hawaii", was published in 1994.

The report followed the guidelines suggested by Bulletin 17B (Interagency Advisory

Committee on Water Data, 1982) for flood frequency analysis and regression techniques.

Log Pearson Type III distribution and methodology was recommended as the default

statistical tool for the analysis of stream flow.

In the report, Wong (1994) further refined the hydrologic regions into three areas:

(1) leeward, (2) windward, and (3) north according to regional drainage-basin and

climatic characteristics (Figure 3.5). The peak discharge data were collected through

water year 1988 for a total of 79 gaging stations on the island of Oahu. The derived

regression equations only apply to gaged sites where peak discharge is not subject to

significant diversion, regulation, and urbanization. Tables 3.1 through 3.3 taken from the

report summarizes Wong's (1994) findings.

77

.21 "40'

21 "20'

HiS"

Base JTO:lified hem U,s. Gedog~l Sur"""idigital data,1 :24,ClX!, 1Q93, Abare. equal areaprojection, stan:lard parallels 21 "1 f1 an:! 21'4f1,central meridian 157"513'

2

157'40'

EXPLANATIONHydrolcgc regon bOUldaryHydrolcgc regon number

o :2 4 6 g MILESIi', I' I I ,

o 2 <I B g KLOOI:TERS

Figure 3.5 Hydrologic Regions, Oahu, Hawaii

Table 3.1 USGS Regression Equations, Region 1 Leeward, Oahu

Equation Bias-Correction FactorEquivalent Years of

RecordQ2 = 3.26(DAU,{)J4)(pl.UlS) 1.115 4.2Q5 = 25.8(DAu.042)(pUJ/J) 1.069 5.8QlO = 73.5(DAu.04{»(pu.{)21) 1.052 8.2Q25 = 217(DAU.04{»(pU.404) 1.040 11.4Q50 = 425(DAU.04')(pU.JM) 1.037 13.7QlOo = 758(DAu.04J)(pU.2lS{» 1.040 15.8

78

Table 3.2 USGS Regression Equations, Region 2 Windward, Oahu


RecordQ2 = 525(DAU./U4) 1.165 2.5Qs = 1140(DAu./4

l.i) 1.138 3.9QlO = 1700(DAu.

/bj) 1.129 5.7

Q2S = 2580(DAU.Ilj) 1.124 8.6Qso = 3360(DAU

.I/b

) 1.125 11.0Q100 = 4250(DAU.III) 1.133 13.6

Table 3.3 USGS Regression Equations, Region 3 North, Oahu


RecordQ2 = 0.00356(DAU.l.i IU)(P22i·l.i:l) 1.036 3.6Qs= 0.151(DAu.l.ijb)(P22/·ju) 1.000 8.3QlO = 1.76(DAu·l.iU:l)(P22/·L4) 1.000 10.2Q2S = 24.8(DAU.III)(P22l lU

) 1.000 10.7Qso = 125(DAU./b:l)(P2241,j~) 1.000 10.5Q100 = 500(DAu.75l.i)(p224u.m) 1.011 10.1

where:

Qt = a flood of return interval equal to t years (cfs)

DA = drainage area (mi2)

P = median annual rainfall (in)

P224 = 2-year, 24-hour rainfall intensity (in)

As stated in Wong's report, the bias-correction factor listed in the table is used to

make adjustment to account for the retransformation bias when logarithmic

transformation is used. This will give the mean value of the predicted peak discharge

instead of median value while the factor is not applied. The regression equation should be

multiplied by the factor to make it more accurate and complete. The equivalent years of

record are for un-gauged site to achieve the reliability of the regression equation. Special

79

attention must be paid to the limitation of using the regression equations. Table 3.4

provides a guideline for such criteria to determine if the regression equations are

applicable. When the parameters do not fall into the ranges, the regression equations are

not suitable to use. The parameter UB in the table stands for Urban Cover, which is the

ratio of urban areas within the drainage basin to the total drainage-basin area. According

to Wong's (1994) report, significant urbanization is defined when UB exceeds 36%. Any

watershed with UB greater than 36% will not be suitable for applying the regression

equations.

Table 3.4 Criteria for Using Regression Equations on Oahu

Hydrologic Region DA (miL) P (in) P224 (in) UB(%)

Region 1 (Leeward) 0.60-45.7 29-239 4.72-8.78 0-32

Region 2 (Windward) 0.03-5.34 52-146 5.62-9.10 0-36

Region 3 (North) 1.11-13.5 66-197 5.21-9.04 0

To better estimate the peak discharge for the gaged sites, Wong (1994) proposed a

weighting technique to improve the end results. The estimate generated from frequency

analysis of gage records is combined with the estimate obtained by applying the

regression equation. The weighting equation for gaged sites is as follows:

Qtg (N) + Qtr (EQ)

Qtw = (N +EQ)

where:

Qtw= weighted average peak discharge at gaged site (cfs) for t-year return interval

80

(3.6)

Qtg = peak discharge from Log Pearson Type III at gaged site (cfs) for t-year return

interval

Qtr = peak discharge from regression equation at gaged site (cfs) for t-year return

interval

N = number of years of gaged records at gaged site

EQ = equivalent years of record associated with regression equation (Table 3.1-3.3)

For ungaged sites on the same stream within the watershed, the derived regression

equations from Tables 3.1 to 3.3 are used with an adjustment factor to account for the

data at the gaged sites. When the drainage area of the ungaged site is more than 50%

smaller or larger than that of the gaged site, the adjustment factor is not applied.

Otherwise, equations (3.7) and (3.8) should be applied.

21DA -DL\IC =R- g (R-1)

U DAg

where:

Qtu = peak discharge at ungaged site (cfs) for t-year return interval

Cu = adjustment factor

Qru = peak discharge from regression equation at ungaged site, ft3/S

R = Qtw at gaged site (cfs)Qtr

DAg = drainage area of the gauged site (mi2)

DAu = drainage area of the ungaged site (mi2)

81

(3.7)

(3.8)

3.2.3 Rational Method

The third method for determining peak discharge is called the rational method. It

is one of the widely known methods for drainage structure design for small urban and

rural watershed. City and County of Honolulu has adopted rational method as the default

method in determining peak discharge for drainage areas of 100 acres or less. Rational

method is included in the "Rules Relating to Storm Drainage Standards" published by

Department of Planning and Permitting, City and County of Honolulu and has been

applied for years by the engineers. The equation for rational method is described as

follows:

Q=CIA (3.9)

where:

Q = peak discharge rate (cfs)

C =runoff coefficient

I =rainfall intensity (in/hr) for duration equal to the time of concentration, Tc

A = drainage area (acres)

The assumption for the rational method is that uniform rainfall intensity is

observed during the storm. The peak discharge is reached when all parts of the drainage

area make contributions to the runoff. The condition will occur at the point where the

storm duration is equal to the time of concentration, Tc' The time of concentration is the

term defined as the travel time for the water to travel through the drainage area from the

most remote point of the drainage area to the point of interest, usually an outlet where

discharge rate is desired.

82

The term, runoff coefficient, considers the effects of various landscapes within the

drainage area in determining the peak discharge. As suggested in the City and County of

Honolulu Storm Design Standard, the runoff coefficient can be estimated from Figure 3.6

for agricultural and open areas and Table 3.5 for built-up areas.

Table 3.5 Runoff Coefficients for Built-Up Areas, Rational Method

Residential Areas C = 0.55 to 0.70

Hotel-Apartment Areas C = 0.70 to 0.90

Business Areas C = 0.80 to 0.90

Industrial Areas C = 0.80 to 0.90

The rainfall intensity can be obtained from Intensity-Duration-Frequency (IDF)

curves if Tc and the design frequency are specified. For Kailua and Waimea Watersheds

IDF curves have been derived in this study as described in Chapter 2. It is assumed that

the frequency of peak discharge is equal to the frequency of the rainfall event. For Tc

calculations, City and County of Honolulu has provided two formulas in its Storm

Drainage Standard for small agricultural drainage basins. Equation (3.10) is for well

forested areas whereas equation (3.11) is for areas with little or no cover. For Tc less than

5 minutes, 5 minutes should be used in determining the rainfall intensity. The formulas

are listed in the following:

Tc =0.0136 * KJon

Tc =0.0078 * KJo77

83

(3.10)

(3.11)

where:

Tc =time of concentration (minutes)

K=LIS

L = maximum length of travel (feet)

S = land slope = H I L

H = elevation difference

The information of drainage area of the watersheds is the same as described in

Section 3.1.1 of this thesis. There is another assumption with the rational method.

According to the publication "Introduction to Hydrology, 4th Edition," the rational

method is most applicable to frequent storms with range of 2- to lO-year return intervals.

Less frequent storms usually come with more severe rainfall amounts, and that causes

wetter antecedent moisture condition. As a result, a larger runoff should be expected from

the storm. A frequency factor is suggested to be applied in the rational method as an

adjustment. The values for the factor are listed in Table 3.6.

Table 3.6 Frequency Factor, Rational Method

Return Interval (years) Frequency Factor

2 - 10 1.0

25 1.1

50 1.2

100 1.25

84

Average Rainfall Intensity In.lHr.2

0.80

~..... BAND 2.....0c: 0.6:::J((-,0......c:Q)

0.4.-u:::=Q)0()

0.2

Band 1

Band 2

Band 3

Band 4

Steep, barren, impervious surfaces

Rolling barren in upper band values, flatbarren in lower part of band, steep forestedand steep grass meadows

Timber lands of moderate to steep slopes,mountainous. farming

Flat pervious surface, flat farmlands,wooded areas and meadows

Figure 3.6 Runoff Coefficients for Agricultural and Open Areas, Rational Method

85

3.3 Peak Discharge from Stream Gage Record in Waimea Watershed

In order to examine which runoff model is better for predicting peak discharge,

three methods are applied to a gauged watershed, namely, Waimea Watershed, on Oahu.

The peak discharge values based on frequency analysis of the actual stream records will

be used as a reference for comparison. Historical stream gage records are obtained from

the USGS website. Frequency analysis based on the stream gage records is performed to

obtain peak discharge for specific return intervals. Since the stream gage records are from

the USGS, the statistical distribution chosen for the frequency analysis will be Log

Pearson Type III Distribution. This is commonly used in the USGS publication, and it is

suggested by the Bulletin 17B. Our own study (results are omitted from the thesis) also

showed that for stream flow records, Log Pearson Type III distribution provides a slightly

better prediction than the Gumbel distribution. This is different to the result for rainfall

analysis where Gumbel distribution is preferred. For engineering applications, since the

differences between the two distributions are small, both distributions are satisfactory for

analyzing both rainfall and steam flow records.

For Waimea Watershed, the main stream is called Kamananui Stream, and a

stream gage station (USGS 16330000) is set up at the downstream outlet near the coast

(Figure 3.7 and 3.8). The annual peak discharge values for the stream gage station record

are summarized in Table 3.7. The procedure of performing Log Pearson Type III

Distribution is described in details in Chapter 2. This section will follow the exact steps,

and the final results and plots of the frequency analysis are presented in Table 3.8 and

Figure 3.9.

86

Figure 3.7 Location of USGS Stream Gage Station 16330000 in Waimea - Part 1

Figure 3.8 Location of USGS Stream Gage Station 16330000 in Waimea - Part 2

87

Table 3.7 Annual Peak Discharge for USGS Stream Gage Station 16330000

Peak PeakWater Discharge Water DischargeYear USGS Station Year USGS Station

16330000 (ds) 16330000 (ds)1958 2570 1979 30601959 2960 1980 85401960 2210 1981 14601961 1020 1982 59601962 3140 1983 23401963 3450 1984 6801964 1590 1985 28001965 3030 1986 10301966 1900 1987 16001967 3000 1988 61001968 5260 1989 42301969 4510 1990 32001970 1650 1991 168001971 3540 1992 N/A1972 1370 1993 30001973 640 1994 34901974 5610 1995 20801975 5270 1996 45401976 2830 1997 39901977 2070 1998 4081978 1920 1999 1120

Table 3.8 Frequency Analysis for USGS Stream Gage Station 16330000

Return Interval Peak Discharge(year) USGS Station 16330000 (cfs)

2 25955 483810 648925 866850 10323100 11980

88

Kamananui Stream, USGS 16330000, Log Peanon Type III

! • Gage Records - Log Pearson Type ill --- 5% Confidence Band -+- 95% Confidence Band I3

100 yrs"- Return IntervalOyrs

25 yrs .I

10yrs

5yrs

-2 I ~,r ./,c 7' I I

2

~

.!~';

!.;. 0

11,-1~

QO\0

-3

100 1000 10000 100000

Peak Discharge (efs)

Figure 3.9 Frequency Analysis for USGS Stream Gage Station 16330000

3.4 Stream Flow Prediction by Applying the SCS TR-20 Method

As described in section 3.2.1, there are many parameters required in order to run

the TR-20 program. A software called ArcGIS is used as an aid to calculate some of the

parameters. This software enables users to open files that contain digitized information.

The information is commonly referred to as a layer. The layer files used in this study can

be downloaded from the Hawaii State GIS Program website or Department of Planning

and Permitting (DPP), City and County of Honolulu website. Some parameters used in

the analysis of TR-20 program are either interpreted from ArcGIS layer information or

calculated manually using appropriate equations.

The parameters for Waimea Watershed are drainage area of the USGS stream

gage station 16330000, weighted runoff Curve Number, time of concentration, design

storm specification. The entire area for Waimea Watershed is roughly 13.8 mi2. The

stream gage is located a little bit inland, so the drainage area of the stream gage will not

cover the entire watershed. The interpreted drainage area from the layer information for

the USGS stream gage 16330000 is 13.1 mi2•

In order to calculate the composite runoff Curve Number for the watershed, two

layers containing soil type and land use information are overlaid with each other (Figure

3.10). The soil type layer defines soil symbol for each soil type. The information on how

to determine hydrologic soil group from soil symbol can be found in page 54 of "Erosion

and Sediment Control Guide for Hawaii". The land use condition of Waimea Watershed

is dominated by two types: conservation and agricultural districts. Simple illustration of

the idea of weighted Curve Number is presented in Figure 3.11. for better understanding.

90

In Figure 3.11, the simple watershed is enclosed within a circle, and it is assumed that the

area above the red line is defined as soil type B where soil type A is below the red line.

The land use condition for the area above the blue line is assumed to be residential area

where the area below the blue line is defined as an agricultural area. It clearly shows that

the entire watershed is divided into 4 subareas, and each subarea has its own soil type and

land use condition which defme a unique runoff Curve Number. Weighted value of the

runoff Curve Numbers from the 4 subareas is calculated, and the end result will be used

as a composite runoff Curve Number for the entire watershed. For land use type of

conservation district, it is assumed to be wood or forest land with good cover in this

study. For agricultural district, it is assumed to be cultivated land without conservation

treatment. Final composite runoff Curve Number for Waimea Watershed is calculated as

69.

Figure 3.10 Land Use Condition - Waimea Watershed

91

Residential

AQ.ricu Itural'-

il

Soil

Figure 3.11 U1ustration ofWeigbted Curve Number

The design stonn duration for the TR-20 program is usually specified to be 24

hours. The design return interval for a hydrologic analysis is usually 100 years (Pl0024).

However, more design return intervals such as 2 years (P224), 10 years (P1024), 25 years

(P2524), and 50 years (P5024) will also be calculated in the TR-20 run. In Chapter. 2~ the.

values OfPI024, P2524, and PlO024 are calculated using the Gumbel Distribution and the LQg:.

Pearson Type ill Distribution as annual series. Values from the Gumbel Distribution are

chosen for Waimea Watershed based on two reasons: 1) By examining the plots, field

data fit slightly better under the Gumbel distribution, and 2) Gumbel Distribution was

adopted in the previous report R-73. The values obtained from Chapter 2 will be

converted to partial series with conversion factor (Table 2.20) for return interval less than

92

10 years before running the TR-20 program. However, there is one factor needed to

consider before using the rainfall values. When running the TR-20 program, the rainfall

amounts should be representative and located at the centroid of the watershed. It is

expected that the rainfall depth will increase toward mountainous area based on the

results from R-73 report. Since the rain gage is located near the downstream end of this

watershed, the use of its data will cause an underestimate of the peak discharge. To

correct this underestimate, an average difference of 2" is estimated from R-73 Report

between the gage location and the middle of watershed. The value will be added to the

results of frequency analysis. The final storm specification for Waimea Watershed after

all adjustments are: P224 = 6.9", PI024 = 10.5", P 2S24 = 12.4", P S024 = 13.9", PI0024 =

15.4".

The rainfall distribution type for Hawaii is defined as Type I according to Figure

3.3. For antecedent moisture conditions (AMe), AMC II is assumed for Hawaii. This is

the most common default condition specified in the TR-20 program if no extreme dry or

wet condition is expected. These two characteristics are specified in the input data sheet

of the TR-20 program.

The calculation of time of concentration for Waimea Watershed will depend

solely on sheet flow and shallow concentrated flow. Open channel flow is not used in the

calculation because exact channel dimension is unknown. In most cases, shallow

concentrated flow is good enough to substitute for the channel portion. The first 300 ft of

the stream is under sheet flow condition (equation (3.1)), where it is located at the top of

the watershed. Manning's roughness value is taken for Woods (dense underbrush, n =

93

0.8) according to Table 3-1 in TR-55 manual. The average velocity of shallow

concentrated flow is calculated using Figure 3.4 or equation (3.3) for unpaved condition.

Time of concentration under the shallow concentrated flow region is obtained by

applying Equation (3.2). Table 3.9 shows the detailed calculation of Tc, and the final

number is estimated to be 3.67 hours.

Table 3.9 Time of Concentration Calculation - SCS TR·20, Waimea Watershed

Flow Horizontal. SlopingRegion Distance Distance Slope Velocity P224 n Tc

(ft) (ft) (ft/ft) (fps) (in) (hr)SF 300 302.2 0.121 6.9 0.8 0.50

SCF 8300 8360.5 0.121 5.61 0.41SCF 4600 4608.5 0.061 3.98 0.32SCF 13200 13208.7 0.036 3.08 1.19SCF 13200 13207.3 0.033 2.95 1.25Sum 39600 39687.2 3.67

With all the parameters calculated for Waimea Watershed, an input data is

prepared to run TR-20 program. The final predicted peak discharge generated from the

output ofTR-20 run is summarized in Table 3.10.

Table 3.10 Predicted Peak Discharge - SCS TR.20, Waimea Watershed

Return Interval Predicted Peak Discharge Recorded Peak Discharge Difference

(Year) (cfs) (cfs) (%)

10 7462 6489 15%

25 9544 8668 10%

50 11215 10323 8.6%

100 12900 11980 7.7%

94

3.5 Stream Flow Prediction by Applying the USGS Regression Method

Waimea Watershed is located on the northwestern part of the island of Oahu. In

order to use the USGS regression equations, the first step is to identify the hydrologic

region of Waimea Watershed. From Figure 3.5, Waimea Watershed belongs in Region 3:

North. Thus, equations provided in Table 3.3 should be used in predicting the peak

discharge. Equations in Table 3.3 involve two parameters: drainage area (DA) and 2-year

24-hour rainfall depth (P224). The drainage area of USGS stream gage station 16330000 is

13.1 me, and P224 is 6.9" as specified in section 3.4.1. In order to use the regression

equations, the parameters must meet certain criteria as stated in Table 3.4. By checking

the values, they fall into the acceptable range. Thus, regression equation will be

considered as a valid tool for flood flow prediction. Table 3.11 provides the peak

discharge for various return intervals determined from application of the regression

equations.

Table 3.11 Predicted Peak Discharge - USGS Regression Equations, Waimea Watershed



10 7291 6489 12%

25 10572 8668 22%

50 13111 10323 27%

100 16405 11980 37%

95

Values in Table 3.11 can be further refined according to Wong (1994). Weighted

value is proposed by combining values from regression equations (Table 3.11) and

frequency analysis (Table 3.8). Equation (3.6) should be used to calculate the weighted

value of the peak discharge. Equivalent years of record for equation (3.6) can be found in

Table 3.3 for watershed located in hydrologic region 3. Number of years of record for

USGS gage station 16330000 is 41 years from 1958 to 1999, except year 1992 where

stream flow data is not available. The weighted peak discharge value for Waimea

Watershed is summarized in Table 3.12.

Table 3.12 Predicted Peak Discharge - Weighted USGS Regression Equations, Waimea Watershed



10 6648 6489 2.5%

25 9062 8668 4.5%

50 10892 10323 5.5%

100 12855 11980 7.3%

These results show that by applying the weighted approach, the accuracy of the

prediction based on the regression equation can be improved.

3.6 Stream Flow Prediction by Applying the Rational Method

The first step to apply the rational method is to determine the size of the drainage

area. The landscape of Waimea Watershed is dominated by conservation district and

96

agricultural district (Figure 3.10). The drainage areas for USGS gage station 1633000

under conservation district and agricultural district are approximated 7838.3 acres and

547.3 acres, respectively, according to the interpretation from GIS files. The total

drainage area is 8385.6 acres (13.1 mi2). Although this area is greater than the normal

empirical upper limit of the drainage area for the rational method to be valid, the method

is still applied here in order to examine how much the method can be "stretched" for

engineering applications in reality.

The next step is to determine the time of concentration for the drainage area under

various landscapes so that the rainfall intensity I can be obtained. Since Waimea

Watershed mostly consists of wide-open forest, Equation (3.10) will be used to determine

the time of concentration. Table 3.13 summarizes the results. The time of concentration

for conservation district and agricultural district are 207.1 minutes and 91.2 minutes

respectively. The larger time of concentration value will be used in the determination of

rainfall intensity to ensure that the rainfall duration is long enough to cover the entire

watershed. The rainfall intensity can be obtained from the IDF curves if the time of

concentration is known. IDF curves for rain gage station Waimea 892 have been derived

and plotted in section 2.5. Since both the TR-20 and Regression Method runoff models

adopt rainfall values from the Gumbel frequency analysis, Figure 2.15 will be used in

determining the time of concentration for rational method for consistency.

The IDF curves obtained from this study for Waimea Station 892 only provide

storm return interval up to 25 years due to lack of 15-minute records for longer periods.

Thus, only the peak discharge of 10- and 25-year frequency will be calculated for

97

comparison with the other two runoff models and with the recorded data. With the known

time of concentration (207 minutes), the rainfall intensity for 10- and 25-year return

interval is approximated 1.4 inlhr and 1.7 inlhr respectively.

Table 3.13 Time of Concentration Calculation - Rational Method, Waimea Watershed

Conservation DistrictHI H2 Horiz. L Slope Sloping L K Tc(ft) (ft) (ft) (ft/ft) (ft) (min)

2240 1200 8600 0.121 8662.7 24910.6 33.01200 920 4600 0.061 4608.5 18679.3 26.5920 440 13200 0.036 13208.7 69267.1 72.6440 0 13200 0.033 13207.3 72339.5 75.0sum 39600 207.1

Agricultural DistrictHI H2 Horiz. L Slope Sloping L K Tc(ft) (ft) (ft) (ft/ft) (ft) (min)

1000 680 4400 0.073 4411.6 16358.7 23.9680 600 1240 0.065 1242.6 4892.0 9.4600 360 5700 0.042 5705.1 27803.0 35.9360 0 4260 0.085 4275.2 14706.5 22.0sum 15600 91.2

The final step is to determine the runoff coefficient. With the known rainfall

intensity, runoff coefficient for agricultural and open areas can be obtained from Figure

3.6. Agriculture district is assumed to fall into band 3 whereas conservation district is in

band 2. The estimated runoff coefficients for agricultural district and conservation district

are 0.3 and 0.5 for the two rainfall intensities. For storm with the 25-year return interval,

a frequency factor of 1.1 will be multiplied to the runoff coefficient to account for the

loss of antecedent moisture for less frequent storms (Table 3.6).

The final calculated results of peak discharge using the rational method are

98

summarized in Table 3.14.

Table 3.14 Predicted Peak Discharge - Rational Method, Waimea Watershed

Peak Discharge, lO-year return interval

Landscape C I (in/hr) A (acres) FactorPredicted Q RecordedQ Difference

(cfs) (cfs) (%)Conservation 0.52 1.4 7838.3 1.0 5706Agricultural 0.24 1.4 547.3 1.0 184 6489 -9.2%

Total 5890Peak Discharge, 25-year return interval

Landscape C I (in/hr) A (acres) FactorPredicted Q RecordedQ Difference

(cfs) (cfs) (%)Conservation 0.53 1.7 7838.3 1.1 7769Agricultural 0.26 1.7 547.3 1.1 266 8668 -7.3%


Landscape C I (in/hr) A (acres) FactorPredicted Q Recorded Q Difference

(cfs) (cfs) (%)Conservation 0.55 2.0 7838.3 1.2 10347Agricultural 0.28 2.0 547.3 1.2 368 10323 3.8%


Landscape C I (in/hr) A (acres) FactorPredicted Q Recorded Q Difference

(cfs) (cfs) (%)Conservation 0.57 2.25 7838.3 1.25 12566Agricultural 0.30 2.25 547.3 1.25 462 11980 8.7%

Total 13028

These results indicate that the rational method provides good estimates toward the

peak flow for Waimea Watershed. One issue must be noticed here that the rainfall

intensity used in Table 3.14 is from rain gage station Waimea 892, which is near the

coastal areas. The actual rainfall reading should be taken at the centroid of the watershed.

Thus, the actual results may be larger in this case since the centroid of Waimea

Watershed is Koolau Range, where more rainfall is expected. However, considering the

99

fact that the drainage area is much greater than the suggested area limit, the predicted

results are quite satisfactory. For more accurate results, the watershed should be divided

into more sub-areas whose area is less than 100 acres. Even the results show good

consistence with the other two methods for Waimea Watershed, the use of the rational

method mayor may not apply to all other watersheds. More research should be

considered in the future.

Comparing among the three different methods, we can see that for Waimea

Watershed, all three methods are able to provide quite accurate predictions for the stream

discharge and they involve relatively the same amount of effort for the calculations. Since

all three methods are empirical methods, and there is always a small uncertainty in the

exact values of the empirical coefficients, the best approach in an engineering design

project would be to try all three methods and compare the results in order to obtain a

more reasonable and reliable prediction for the stream discharge.

100

CHAPTER 4. SUMMARY AND CONCLUSION

Rainfall frequency analysis was carried out for six selected rain gage locations,

namely, Hawaii Kai Gold Course, Kailua Fir Station, Kahuku, Makaha, Pupukea Height

and Waimea on Oahu Island in Hawaii. Rainfall intensity of return periods of 2, 10, 50

and 100 years was determined. The predicted results from this study based on newer and

much longer records were compared with the results from two earlier reports in 1962 and

1984. The comparison revealed that the present results are very similar to the previous

results and no significant changes were observed. Specifically, the average difference

between the present result and the two earlier results is 13% (compared with the 1984

results) and 26% (with the 1962 results). The main reason for the relatively larger

difference between the present result and the 1962 result is that the rainfall intensity maps

presented in the 1962 report are very small and are of low resolution. It is very difficult to

read the results accurately from this particular report. In other words, the earlier 1962

and 1984 results are still satisfactory as far as the accuracy of rain data and statistical

analysis are concerned. However, they can be updated and improved by presenting the

results in clearer table format.

In order to further study the effect of data record length on rainfall frequency

analysis, forty sets of shorter records of 15, 20, 30 and 40 years were randomly

constructed based on two available 82-year and 84-year actual records at two different

locations on Oahu. Rainfall intensity of 80-year return period was predicted based on the

shorter records by applying the Gumbel distribution. The predicted values were compared

101

with the actual values based on the original 82-year and 84-year records. Our results

show that the average relative error in the prediction based on the shorter records is

similar and it ranges from 9% (40-year record) to 21% (IS-year record). Although the

averaged error is similar, longer records (e.g., 30-year record) provide more consistent

and reliable predictions. We found that for predicting the rainfall intensity of 80-year

return period for the two rain gage stations, a 30-year data record is sufficient. However,

more rain gage stations and trials should be included in future studies to have general

conclusion for the entire Oahu Island.

Intensity-duration-frequency (IDF) curves for two watersheds, namely, Kailua

and Waimea Watersheds, were developed. The factor for converting I-hour rainfall depth

to rainfall intensity of other durations was obtained and compared with the empirical

value given in the City and County's drainage design manual. Comparison showed some

differences between the actual and the empirical values for this converting factor, and the

difference is found to vary between different locations and different durations. On

average, the difference is relatively small, and our results indicate that the empirical

converting factor is acceptable for engineering practice.

Three different methods, namely, the Soil Conservation Services' TR-20 method,

the USGS regression method, and the rational method, were applied to predict the stream

flow of different return frequency for gaged Kamananui Stream in Waimea Watershed as

a case study. The objective was to examine the accuracy and efficiency of the three

methods in predicting stream flow in Hawaii. The predicted 10-, 25-, 50-, and 100-year

flood discharge was compared among the three methods and with the measured data

102

based on the stream gage record. Our results showed that the three methods provide quite

consistent results, and the predicted results agree with the measured data very well. As

for the amount of efforts involved, the three methods seem to be equally efficient. Since

all three methods are empirical methods, and there is always a small uncertainty in the

values of the empirical parameters, the best engineering practice would be to apply all

three methods in each design and determine the "best reliable" prediction after comparing

the results from the three methods and seeking the most consistent result.

103

.....~

Appendix A: Detailed Results of Sensitivity Analysis

Table AI: Sensitivity Analysis Results for Waimea 892

Waimea 892 actual rainfall depth of 80-year return period=12.96"

15-year data 20-year data 30-year data 40-year dataRank predicted %Diff predicted % Diff predicted % Diff Ipredicted % Diff CDP

1 19.4 49.9 17.9 38.0 16.9 30.7 16.3 26.0 0.022 18.3 41.2 17.2 32.5 16.2 25.2 16.0 23.5 0.053 18.2 40.1 16.8 29.5 15.7 21.5 15.4 19.0 0.074 18.0 39.0 16.6 28.3 15.6 20.6 15.4 18.9 0.105 17.6 36.0 16.5 27.6 15.6 20.4 15.3 18.1 0.126 17.5 34.8 16.2 25.3 15.3 18.1 15.1 16.9 0.157 17.2 33.0 16.2 25.1 15.3 17.7 15.1 16.4 0.178 17.1 31.6 16.0 23.8 15.2 17.6 15.1 16.1 0.209 16.9 30.8 16.0 23.5 15.1 16.9 15.0 16.0 0.2210 16.7 29.2 15.9 23.1 15.1 16.3 15.0 15.7 0.2411 16.7 29.0 15.9 22.3 15.1 16.2 14.9 14.6 0.2712 16.3 25.9 15.6 20.2 15.0 15.8 14.7 13.4 0.2913 16.0 23.6 15.6 20.1 14.9 15.0 14.5 11.6 0.3214 15.9 22.5 15.5 19.5 14.9 14.8 14.5 11.6 0.3415 15.8 22.0 15.3 17.9 14.7 13.6 14.4 11.3 0.3716 15.8 21.7 15.1 16.7 14.6 12.3 14.4 11.0 0.3917 15.6 20.6 15.1 16.3 14.6 12.3 14.3 10.0 0.4118 15.5 19.5 15.1 16.2 14.5 12.2 14.0 8.4 0.4419 15.4 19.1 15.0 15.8 14.4 11.4 14.0 8.3 0.4620 15.2 17.3 14.9 14.6 14.3 10.4 14.0 8.1 0.49

......oVl

Table AI: Sensitivity Analysis Results for Waimea 892, Continue I

21 14.8 14.3 14.5 11.9 14.2 9.7 13.8 6.8 0.5122 14.8 14.1 14.5 11.8 14.2 9.6 13.6 5.2 0.5423 14.7 13.7 14.4 10.8 14.1 9.1 13.5 4.6 0.5624 14.5 11.8 14.2 9.6 14.0 8.3 13.5 4.4 0.5925 14.2 9.7 14.2 9.5 14.0 7.8 13.5 3.8 0.6126 14.1 8.8 14.2 9.4 13.9 7.5 13.4 3.4 0.6327 14.0 8.2 14.1 9.2 13.7 6.1 13.4 3.3 0.6628 13.7 5.8 14.1 8.9 13.7 5.7 13.3 2.4 0.6829 13.6 5.1 13.8 6.8 13.7 5.7 13.3 2.4 0.7130 13.5 4.0 13.8 6.2 13.6 5.0 13.3 2.3 0.7331 13.3 3.0 13.7 6.1 13.6 5.0 13.3 2.3 0.7632 13.3 2.9 13.7 5.4 13.6 4.7 13.2 2.2 0.7833 13.3 2.5 13.6 4.8 13.5 4.1 13.2 1.6 0.8034 13.3 2.4 13.5 4.4 13.5 3.9 13.1 1.5 0.8335 13.2 2.1 13.5 4.4 13.4 3.7 13.1 1.3 0.8536 13.2 1.9 13.4 3.5 13.3 2.8 13.1 1.0 0.8837 13.1 1.5 13.3 2.9 13.2 2.2 13.1 1.0 0.9038 13.1 1.5 13.3 2.7 13.2 2.1 13.1 0.9 0.9339 13.1 1.1 13.2 1.8 13.2 1.7 13.0 0.4 0.9540 13.0 0.0 13.0 0.6 13.2 1.6 13.0 0.1 0.98

standard deviation 13.9 9.6 7.1 7.2mean 17.5 14.7 11.1 8.6

......o0\

Table A2: Sensitivity Analysis Results for Kahuku 912

Kahuku 912 actual rainfall depth of 80-year return period =12.17" IIS-year data 20-year data 30-year data 40-year data

Rank predicted % Diff predicted % Diff Ipredicted % Diff Ipredicted % Diff CDP1 20.7 70.1 18.4 51.3 18.0 47.5 16.5 35.5 0.022 20.0 63.9 18.4 51.2 16.6 36.5 15.2 24.7 0.053 19.4 59.3 18.2 49.4 16.0 31.7 15.0 23.1 0.074 19.3 58.8 18.1 48.7 15.8 29.7 14.9 22.7 0.105 19.2 58.2 18.1 48.4 15.6 28.3 14.8 21.8 0.126 16.2 33.4 17.2 41.4 15.4 26.9 14.7 20.8 0.157 16.1 32.5 17.0 39.8 15.3 25.9 14.7 20.7 0.178 16.1 32.0 16.8 38.4 15.3 25.8 14.7 20.5 0.209 16.0 31.8 16.7 37.6 15.2 24.6 14.6 20.3 0.2210 15.9 30.5 16.6 36.8 15.1 24.4 14.6 19.7 0.2411 15.8 29.5 16.6 36.5 15.1 24.4 14.5 19.4 0.2712 15.8 29.5 16.4 34.4 15.1 24.2 14.5 19.0 0.2913 15.6 28.5 16.1 32.6 15.1 24.1 14.5 18.9 0.3214 15.6 28.5 16.0 31.4 14.9 22.5 14.1 15.7 0.3415 15.4 26.4 15.9 30.7 14.8 21.8 14.1 15.7 0.3716 15.2 25.1 15.8 30.2 14.5 19.3 14.0 15.2 0.3917 14.7 21.0 15.4 26.8 14.5 18.9 14.0 14.7 0.4118 14.4 18.7 15.1 24.3 14.4 18.6 13.9 14.5 0.4419 14.4 18.0 14.6 20.0 14.4 18.3 13.9 14.4 0.4620 14.3 17.8 14.0 14.9 14.2 16.9 13.9 14.3 0.49

-o-.l

Table AI: Sensitivity Analysis Results for Kahuku 912, Continue 1

21 14.2 16.5 13.7 12.8 14.2 16.3 13.9 14.3 0.5122 14.0 14.7 13.4 10.3 14.2 16.3 13.9 14.1 0.5423 13.8 13.5 13.4 10.0 14.1 15.9 13.8 13.8 0.5624 13.7 12.7 13.4 9.8 14.1 15.8 13.8 13.6 0.5925 13.5 11.1 13.3 9.5 14.1 15.7 13.7 12.4 0.6126 13.4 9.7 13.1 7.3 14.0 15.2 13.6 12.1 0.6327 13.3 9.6 13.0 7.0 14.0 15.0 13.6 12.0 0.6628 13.1 8.0 13.0 6.9 14.0 14.9 13.6 11.8 0.6829 13.1 7.6 13.0 6.7 13.9 14.5 13.6 11.7 0.7130 13.1 7.4 12.8 5.1 13.7 12.2 13.5 11.0 0.7331 12.8 5.4 12.7 4.3 13.3 9.4 13.4 10.1 0.7632 12.7 4.0 12.6 3.9 13.2 8.6 13.1 8.0 0.7833 12.7 4.0 12.6 3.9 13.2 8.4 13.1 7.4 0.8034 12.6 3.6 12.6 3.7 13.2 8.3 12.9 6.3 0.8335 12.6 3.4 12.6 3.6 13.2 8.1 12.9 6.3 0.8536 12.6 3.2 12.5 2.9 13.1 7.8 12.9 5.7 0.8837 12.5 2.4 12.4 2.2 12.5 2.3 12.8 5.3 0.9038 12.4 2.2 12.4 1.7 12.4 2.0 12.7 4.3 0.9339 12.3 1.1 12.4 1.5 12.3 1.0 12.6 3.6 0.9540 12.3 1.0 12.3 1.0 12.3 0.8 12.4 2.2 0.98

standard deviation 18.8 17.2 9.9 6.8mean 21.4 21.0 18.0 14.4

Appendix B: TR-20 Input File for Waimea Watershed

******************80-80 LIST OF INPUT DATA FOR TR-20 HYDROLOGY******************

JOB TR-20 FULLPRINT SUMMARTITLE 001 FN:WaimeaTT.txt (My Data)TITLE 002 SCS (10-, 25-, 50- & 100-YR, 24-HR STORM), Waimea Watershed6 RUNOFF 1 001 1 13.1 69.0 3.670 1 1 1

ENDATA7 INCREM 6 0.107 COMPUT 7 001 001 0.0 15.40 1.0 1 2 1 1 100year

ENDCMP 17 COMPUT 7 001 001 0.0 13.90 1.0 1 2 1 2 50year

ENDCMP 1,..... 7 COMPUT 7 001 001 0.0 12.40 1.0 1 2 1 3 25year000 ENDCMP 1

7 COMPUT 7 001 001 0.0 10.50 1.0 1 2 1 4 10yearENDCMP 1ENDJOB 2

*******************************END OF 80-80 LIST********************************

The text format for the TR-20 input file shown in Appendix B is "Courier New". The purpose for doing this is to meet the

requirements of the TR-20 program. Since TR-20 is written in FORTRAN computer language, it is important to line up each

column in order to run the program properly. Certain columns are designated to carry out specific commands.

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