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Pilbara Region Flood Frequency Analysis Review
By Jim Davies and Edwin Yip
JDA
Date: 12 November 2012
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Outline of the Presentation
• Introduction
• Study Area and Flow Data
• Methodology and Results
• Conclusions
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Outline of the Presentation
• Introduction
• Study Area and Flow Data
• Methodology and Results
• Conclusions
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Outline of the Presentation
• Introduction
– Background
– Previous Studies
– Scope of this Study
– Source of Information
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Introduction
Background
•Regional method is for ungauged catchment flood estimation
•Frequency analysis is estimation of how often a specified event will occur
•Extreme environmental event such as floods, have severe consequences for society
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Introduction
Background (Cont.)
•Couple of advance statistical techniques were developed since the last two decades after the publication of ARR1987,
–L-moments were introduced in 1990’s.
•The aim of this study is to review the ARR1987 Index-flood Method of Pilbara utilizing:-
–advance statistical techniques, and
–flow measurement records up to 2012
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Introduction
Previous Studies
Estimation of design peak discharge for ungauged catchments:
• 1972 US Bulletin 17 – LPIII
• 1975 UK Flood Studies Report – GEV
• 1987 Australia AR&R – LPIII
• 1997 “Regional Frequency Analysis” – Complete Procedure
by Hosking & Wallis - L moments
- Screening of Data
- Regions
- Choice of Distribution
- Estimation of Frequency
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Introduction
Pilbara Region
Gascoyne Region (firm recommendations
of design discharges
were not made in
ARR1987)
Regions defined in ARR1987
Pilbara Region + Gascoyne Region
= Drainage Division 7
25 years out of date now
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Introduction
Pilbara Index-flood Method (ARR1987)
•was developed utilizing 13 stream gauging stations in Pilbara Region
•Methodology
– Annual Exceedance Series
– Log-Normal distribution (assumed the generalised skew coefficient was zero)
– Method of Product-Moments
– All 13 catchments to form one Pilbara region
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Introduction
Pilbara Index-flood Method (ARR1987) (Cont.)
•Frequency Factors are depending on:
– Catchment Area
– ARIs
ARI 2 yrs 5 yrs 10 yrs 20 yrs 50 yrs
Area (km2)
Frequency Factors
1 0.55 1.00 1.58 2.40 3.90
10 0.52 1.00 1.70 2.77 4.90
100 0.50 1.00 1.81 3.20 6.30
1,000 0.48 1.00 1.94 3.70 7.90
10,000 0.46 1.00 2.08 4.25 9.90
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Introduction
Pilbara Index-flood Method (ARR1987) (Cont.)
•Index-flood:
– Design Discharge of 5-year ARI [m3/s]
Q5 = 6.73 x 10-4 A0.72 P1.51
•Parameters in Design Discharge Equation:
– Catchment factor: Catchment Area (A) [km2]
– Climatic factor: Average Annual Rainfall Depth over the Catchment Area (P) [mm]
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Introduction
L-Moments (Hosking & Wallis, 1997)
• Sample moment statistics especially skewness and Kurtosis not reliable (biased) as algebraically bounded.
• “L-moments” are linear combinations of order statistics – less subject to bias.
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Introduction
Software
•R-Project –with L-moments Packages “lmom” and “lmomRFA”
•The R-Project and L-moment Packages are freely available
–Website: http://www.r-project.org/
•J. R. M. Hosking is the developer and maintainer of the L-moment Packages
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Introduction
EA AR&R Revision Projects: Project 5
“Regional Flood Methods”
Stage 2 Report
PS/S2/015
June 2012
By University Of Western Sydney
To test generic techniques for all Australia
(WA Contributors: JR, NC, LP, MP, JG)
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Introduction
Project 5 Stage 2 Report June 2012,
General:
• RFFA methods preferred to PRM
• QRT and PRT perform similarly
• PRT preferred due to smoothness
• ROI outperforms fixed regions
• RFFA requires only area and design rainfall intensity data (easy and simple)
• Arid and semi-arid regions have insufficient data for RFFA; recommends simplified RFFA (4 regions)
• Trends will be analyzed in Stage III (expected to be adjustment of ARI’s
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Introduction
Project 5 Stage 2 Report June 2012
Western Australia Specific
–146 catchments (gauging stations) •Kimberley: 14 stations
•Pilbara: 12 stations
•South West: 120 stations
–Area Range 0.1 to 7,405 km2
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Introduction
Project 5 Stage 2 Report June 2012
• Pilbara Region 0.1 to 1,000 km2
• Fixed region (all 12 stations)
• QRT Q2, Q5, Q10, Q20, Q50, Q100
– Function of Catchment Area and Rainfall Intensity
• PRT M, S, G
– Function of Catchment Area, Rainfall Intensity, forest area, and stream density
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Introduction
Project 5 Stage 2 Report June 2012
Source: Rahman, A., Haddad, K., Zaman, M., Ishak, E., Kuczera, G. and Weinmann, P. E. (2012). Regional flood methods for Australia, ARR Revision Project 5 Stage 2 Report, Engineers Australia, Report No. P5/S2/015
Flow records from 12 gauging
stations in Drainage Division 7
were selected and analyzed in
“ARR Revision Projects -
Project 5 Regional Flood
Methods Stage II”
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Introduction
Scope of this Study
•To develop design equations for Index-flood (Q5) to estimate design peak discharges for ungauged catchments
–utilizing the updated stream flow measurement records
•To review the frequency factors of ARR1987 Index-flood method to Pilbara
–utilizing the updated stream flow measurement records
–utilizing advance statistical techniques
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Introduction
Scope of this Study (Cont.)
•To compare the design discharges between this study and other studies
–ARR1987
–“Design Flood Estimation in Western Australia” by David Flavell (2012) (Flavell 2012)
–“ARR Revision Projects - Project 5 Regional Flood Methods Stage II” by Ataur Rahman and others (2012) (ARR P5 S2)
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Introduction
Source of Information
•Department of Water
– Daily maximum flow measurement records
– Location of stream gauging stations
•Bureau of Meteorology
– Average Annual Rainfall Depth
•ARR1987
– Design Rainfall Intensity
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Outline of the Presentation
• Introduction
• Study Area and Flow Data
• Methodology and Results
• Conclusions
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Study Area and Flow Data
Study Area
•Whole Drainage Division 7 (i.e. Division of Indian Ocean) including 10 River Basins as listed follow:-
– Greenough River (701),
– Murchison River (702),
– Wooramel River (703) ,
– Gascoyne River (704),
– Lyndon-Minilya Rivers (705),
– Ashburton River (706),
– Onslow Coast (707),
– Fortescue River (708),
– Port Hedland Coast (709), and
– De Grey River (710)
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Study Area and Flow Data
706 - Ashburton River
702 - Murchison River
703 - Wooramel River
704 - Gascoyne River
705 - Lyndon-Minilya
Rivers
701 - Greenough River
707 - Onslow Coast
709 - Port Hedland Coast
710 - De Grey River
708 - Fortescue River
- Selected Stations (60)
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Study Area and Flow Data
Source: Flavell, D. 2012, “Design flood estimation in Western Australia”, Australian Journal of Water Resources, Vol. 16, No. 1, pp. 1-20, http://dx.doi.org/10.7158/W11-865.2012.16.1 .
Yule River (1975)
Sherlock River (1984) Portland River (1984)
Nullagine River (2002)
Sherlock River (1971)
Robe River (2009)
Fortescue River (2004)
Ashburton River
(1997)
Maximum Floods in Pilbara Region
World Maximum Flood
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Study Area and Flow Data
Rank Catchment Area (km2)
River Gauging
Station No.
1 (largest) 86,777 Murchison River 702001
2 74,432 Gascoyne River 704139
3 71,387 Ashburton River 706003
4 71,212 Gascoyne River 704193
5 69,278 Gascoyne River 704194
6 50,007 De Grey River 710003
7 43,098 Ashburton River 706209
8 34,775 Gascoyne River 704195
9 29,752 Fortescue River 708006
10 19,613 Lyons River 704196
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Study Area and Flow Data
Rank Catchment Area (km2)
River Gauging
Station No.
51 198 Sthn Fortescue River 708004
52 174 Robe River 707001
53 128 Tanberry Creek 709006
54 78 Sherlock River 709009
55 77 Five Mile Creek 710002
56 50 Harding River 709002
57 49 Harding River 709007
58 41 Kanjenjie Creek Trib. 708009
59 34 Buller River 701006
60 (smallest) 0.13 Nokanena Brook Catch
701601
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Study Area and Flow Data
Design Rainfall Intensity from ARR1987 [mm/hr] (1hour duration, 2-years ARI)
35
30
27.5
25
22.5
20
20
18 16
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Study Area and Flow Data
DoW Hydrographic Work – Rating Curve
•“Water Depth” vs “Flow Discharge” derivation using discharge measurement and HEC-RAS modelling
•See paper in AHA Conference 2010 Perth by:-
–Michael Harris and Leith Bowyer
–Ross Doherty
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Study Area and Flow Data
Ashburton River
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Study Area and Flow Data
Ashburton River
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Study Area and Flow Data
Maitland River
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Study Area and Flow Data
Maitland River
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Outline of the Presentation
• Introduction
• Study Area and Flow Data
• Methodology and Results
• Conclusions
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Methodology and Results
Methodology - For Extreme Discharges
1)Extract the AM series of stations in study area from flow measurement data of DoW
–The quality of the measurement records were reviewed, poor quality records were discarded
–The data in AM series was reviewed to ensure no two sequent data is due to same storm event
–Only the stations with AM series containing at least 10 years of data are selected in this study
(60 out of 90 stream gauging stations were selected in this study)
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Methodology and Results
Methodology - For Extreme Discharges (Cont.)
2)Divided 3 hydrological regions according to catchment areas, the 3 regions are (after Hosking and Wallis
(1997)):-
–Small Area Region (19 gauging stations) – “S”:
•catchment area ≤ 1,000 km2
–Medium Area Region (25 gauging stations) – “M”:
•1,000 km2 < catchment area ≤ 10,000 km2
–Large Area Region (16 gauging stations) – “L”:
•catchment area > 10,000 km2
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Methodology and Results
Hosking and Wallis (1997), page 180
“Nonetheless, we emphatically reject the possibility of
performing regional frequency analysis with the entire set of sites being treated as a single region. The main reason is that the theory and practice of hydrology imply that the frequency distribution is likely to depend on the drainage area of the basin. Regional frequency analysis should therefore be applied only to regions whose basins cover a fairly small range of drainage area.”
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Methodology and Results
Hosking and Wallis (1997), page 180
“A further point is that in regional frequency analysis
there is little to be gained by using regions containing more than about 20 sites. A reasonable starting point for regional frequency analysis would therefore be a subdivision of the set of sites, according to their drainage areas, into groups of not much more than 20.”
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Methodology and Results
Methodology - For Extreme Discharges (Cont.)
3)Sub-divide regions “S”, “M”, and “L” according to their statistical homogeneity,
– Gauging stations with H-statistic < 2.0 were considered that they could belong to same sub-region
– The number of stations in each sub-regions should not be much more than 20
– discordance test based on L-moment ratios was performed to ensure no existence of discordancy dataset in sub-regions
(sub-regions S1 to S3; M1 to M3; L1 to L3; were formed)
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Methodology and Results
Methodology - For Extreme Discharges (Cont.)
4)Best-fitted frequency distribution for each sub-regions
– The best-fitted frequency distribution was considered to be the one with the smallest absolute value of Z-statistic
– Candidate frequency distributions are:-
• Generalized Logistic,
• Generalized Extreme Value,
• Generalized Normal,
• Pearson Type III, and
• Generalized Pareto
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Methodology and Results
Sub-Region Name
Selected Gauging Stations
H-Statistic (< 2.0)
Best-fitted Distribution (Z-Statistic) (close to 0)
S-1
706207*, 709002, 709006, 709007, 709009, 709010, 710004
1.326 Pearson Type III
(0.108)
S-2 701003, 701004, 701005, 701006, 701601, 704002
1.733 Generalized
Logistic (-0.350)
S-3 704001, 704003, 704004, 707001, 708009, 708227
1.682 Generalized
Pareto (1.384)
* see later plot
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Methodology and Results
Sub-Region Name
Selected Gauging Stations
H-Statistic (< 2.0)
Best-fitted Distribution (Z-Statistic) (close to 0)
M-1
703001, 705001, 705002, 707005, 710001, 710204, 710229
0.520 Generalized
Pareto (2.826)
M-2
701007, 701008, 701009, 701010, 701013, 701014, 707002, 707004, 708001, 708011, 708013, 708014, 708016
0.931 Generalized
Logistic (-0.172)
M-3 709001, 709003, 709004, 709005, 709008
0.010 Pearson Type III
(0.671)
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Methodology and Results
Sub-Region Name
Selected Gauging Stations
H-Statistic (< 2.0)
Best-fitted Distribution (Z-Statistic) (close to 0)
L-1 701002, 701011, 701012, 702001, 703002
0.548 Pearson Type III
(0.024)
L-2
704139, 704193, 704195, 704196, 706003, 706209, 710003
0.855 Generalized
Pareto (-0.260)
L-3 708002, 708003, 708015, 708223 1.195
Pearson Type III (0.998)
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Methodology and Results
Methodology - For Extreme Discharges (Cont.)
5)Estimate parameters of each selected station for their best-fitted frequency distribution
6)Estimate the extreme discharges (QY, Y = 2-, 5-, 10-, 20-, 50-, 100-year ARI) of every stations in each sub-regions
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Methodology and Results
Methodology - For Frequency Factors
7)Define the peak discharge in 5-year ARI (i.e. Q5) as the “index-flood”, in regions “S”, “M”, and “L”
8)Make the peak discharges dimensionless by dividing them by Q5, (i.e. QY / Q5)
9)Calculate different Frequency Factors for different ARIs in each region,
– “Frequency Factor” is the mean of [QY / Q5] over all stations and in regions S, M, and L
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Methodology and Results
Medium Area Region
Small Area Region
Large Area Region
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Methodology and Results
Methodology - For Design Discharge Equation (Q5)
10)Catchment factors and climate factors for each selected station:-
–Catchment Area (A) [km2]
–Average Annual Rainfall Depth (P) over the catchment area between year 1946 to year 2005 [mm/year]
–Design Rainfall Intensity (IDuration, ARI) over catchment area [mm/hr] of ARI 2- and 50-year (1hr, 12hrs, 72hrs)
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Methodology and Results
Methodology - For Design Discharge Equation (Q5) (Cont.)
11)Develop design discharge equation for Design Discharges of 5-year ARI (Q5) in regions S, M & L using catchment factors and climate factors,
–Stepwise Variable Selection and Multiple Variables Linear Least Square Regression were performed
–The reasonability and simplicity of the design discharge equation are considered
–The number of climate and catchment factors kept to a minimum, they should also be easy to obtain by end-users.
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Methodology and Results
Results (Cont.)
For Small Size Region
(i.e. catchment area ≤ 1,000 km2)
Design Discharge Equation:
Q5 = 8.26*10-9 A0.703 I1hr,2yrs5.798
Frequency Factors:
ARI 2 yrs 5 yrs 10 yrs 20 yrs 50 yrs 100 yrs
FF 0.34 1.00 1.64 2.43 3.84 5.37
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Methodology and Results
Design Equation of Q5 in “ARR Revision Projects - Project 5 Regional Flood Methods Stage II”
ln(Q5) = 3.90 + 0.48 [ln(A) – 4.71] + 7.20 [ln(I12hrs, 2yrs) – 1.47]
=> Q5 = 1.30x10-4 A0.48 I12hrs,2yrs7.20
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Methodology and Results
Results (Cont.)
For Medium Size Region
(i.e. 1,000 km2 < catchment area ≤ 10,000 km2)
Design Discharge Equation:
Q5 = 2.72*10-7 A0.797 I1hr, 50yrs3.506
Frequency Factors:
ARI 2 yrs 5 yrs 10 yrs 20 yrs 50 yrs 100 yrs
FF 0.33 1.00 1.71 2.67 4.59 6.87
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Methodology and Results
Results (Cont.)
For Large Size Region
(i.e. catchment area > 10,000 km2)
Design Discharge Equation:
Q5 = 4.26*10-6 A0.783 I1hr, 50yrs2.815
Frequency Factors:
ARI 2 yrs 5 yrs 10 yrs 20 yrs 50 yrs 100 yrs
FF 0.27 1.00 1.76 2.64 3.98 5.13
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Outline of the Presentation
• Introduction
• Study Area and Flow Data
• Methodology and Results
• Conclusions
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Conclusions
Conclusions
•Design discharges from JDA 2012 can be applied to whole Drainage Division 7
– ARR1987 and Flavell 2012 cannot generate satisfactory design discharges in Gascoyne Region
– Doubt about equations from ARR P5 S2 can be applied in river basin 702, 703, 705, and 710
• No stations were selected at those river basins in the equations development
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Conclusions
Conclusions (Cont.)
•Design discharges from JDA 2012 can be applied to a wide range of catchment area
– ARR P5 S2 cannot generate satisfactory design discharges in large catchment area
• Stations with maximum catchment area of
1,000 km2 were selected
• The catchment areas in Pilbara are large in particular in downstream areas, say as large as 80,000 km2
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Conclusions
Conclusions (Cont.)
•The design equations of JDA 2012 is simple and easy to apply,
– only catchment area and design rainfall intensity are required in the design discharge equations
– The parameters are easy to obtain
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Conclusions
Conclusions (Cont.)
•ARR 1987 often over estimated the data (except river basins 709, 710)
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Study Area and Flow Data
706 - Ashburton River
702 - Murchison River
703 - Wooramel River
704 - Gascoyne River
705 - Lyndon-Minilya
Rivers
701 - Greenough River
707 - Onslow Coast
709 - Port Hedland Coast
710 - De Grey River
708 - Fortescue River
- Selected Stations (60)
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Conclusions
Conclusions (Cont.)
•Flavell (2012) may mis-represent due to changes to measured DoW Flow Data
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Conclusions
Conclusions (Cont.)
•Method will need recalibrate for revised IFD, published at H&WR Symposium November 2012