REGIONAL FLOOD
METHODS
Update on Pilot Studies
Australian Rainfall and Runoff
A guide to flow estimation
OVERVIEW
• Project team
• RFFA methods in ARR 1987
• Pilot study results for Victoria
• Status reports for other states
Australian Rainfall and Runoff
A guide to flow estimation
1
PROJECT TEAM
• Dr Ataur Rahman
• Mr Mark Babister
• Mr Khaled Haddad
• Dr William Weeks
• Associate Professor
James Ball
• Dr David Kemp
• WA Representatives
• Mr Erwin Weinmann
• Professor George
Kuczera
Australian Rainfall and Runoff
A guide to flow estimation
METHODS IN AR&R 1987
• Probabilistic Rational Method
– Vic & Eastern NSW
– Frequency factors depend on elevation for
six zones A-F for Eastern NSW.
• Multiple regression relationship
– Western NSW
• Quantile Regression
– ACT
Australian Rainfall and Runoff
A guide to flow estimation
2
METHODS IN AR&R 1987
• Qld
– No general method meets the primary
criterion of being based on sufficient
observed flood data.
– Main Roads Department Rational Method not easy to apply.
– Department of Primary Industries Rational
Method - based on little/no observed
streamflow records.
Australian Rainfall and Runoff
A guide to flow estimation
METHODS IN AR&R 1987
• SA - South East Region
– Probabilistic Rational Method (Based on
observed data from 20 catchments).
– Department of Agriculture Method - Index
type approach (based on floods data from
6 small agricultural catchments).
Australian Rainfall and Runoff
A guide to flow estimation
3
METHODS IN AR&R 1987
• SA – Northern and Western Region
(Based on very little observed data)
– Rational Method
– Bankfull frequency method – Method of
western NSW by McDermott and Pilgrim
(1983).
– Regional Flood Frequency Method –
Based on records of 3 catchments.
Australian Rainfall and Runoff
A guide to flow estimation
METHODS IN AR&R 1987
• WA
– Five regions.
– Rational method & Index flood method.
– Methods were based on data from 12-28
catchments.
• NT
– Methods were based on limited data.
– Rational method.
Australian Rainfall and Runoff
A guide to flow estimation
4
METHODS IN AR&R 1987
• Western Tasmania
– Regional flood frequency method.
• Eastern Tasmania
– No design information based on observed
data is available. Turner’s (1961)
procedure is suggested.
Australian Rainfall and Runoff
A guide to flow estimation
METHODS TESTED
• Probabilistic Rational Method
• Quantile Regression Technique
– Ordinary least squares (OLS); and
– Generalised least squares (GLS).
Australian Rainfall and Runoff
A guide to flow estimation
5
PROBABILISTIC RATIONAL
METHOD
CY is the central component of PRM
QY = 0.278 CY I t ,Y A
c
Limitations:
• Location based interpolation for CY
• Limited independent testing.
• Limited data on prediction uncertainty.
Australian Rainfall and Runoff
A guide to flow estimation
PROBABILISTIC RATIONAL
METHOD
Advantages of PRM:
– Easy to apply
– Simple regional approach with meaningful
independent variables
– CY integrates effects of other flood
generation and attenuation factors in the
equation.
Australian Rainfall and Runoff
A guide to flow estimation
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QUANTILE REGRESSION
• QRT can be expressed as:
QT = aB bC c D d
– B, C, D, … are variables (catchment area,
main stream slope, rainfall intensity) and a, b,
c, … are regression coefficients to be
estimated by:
• OLS (traditionally)
• GLS (preferable)
Australian Rainfall and Runoff
A guide to flow estimation
PRM and QRT
• PRM was developed
– FFY = CY/C10
– C10 contour was mapped using MAPINFO
• QRT - OLS method was developed
using SPSS
• QRT - GLS method was developed
using Statistical Package R.
• Independent testing was undertaken.
Australian Rainfall and Runoff
A guide to flow estimation
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INTRODUCTION
Typical problems in streamflow data
collation include:
• Unrepresentative sites;
• Missing records; and
• Outliers, trends and rating curve
extrapolation errors.
Australian Rainfall and Runoff
A guide to flow estimation
SELECTION OF CANDIDATE STATIONS
Initially 415 candidate catchments
selected from Victoria based on the
following criteria:
1.
2.
3.
4.
5.
6.
Catchment Area (up to 1000 km2)
Record Length (initially 10 years was cut-off)
Regulation
Urbanisation
Landuse change
Quality of data
Australian Rainfall and Runoff
A guide to flow estimation
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LOCATIONS (Vic)
Study area and geographical distributions of the candidate study catchments
Australian Rainfall and Runoff
A guide to flow estimation
INFILLING MISSING
RECORDS
• Method 1: Comparison of monthly
instantaneous maximum (IM) data with
monthly maximum mean daily (MMD)
data for the year with data gap
Australian Rainfall and Runoff
A guide to flow estimation
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INFILLING MISSING
RECORDS
Method 2 - Infilling by Regression
y = 1.8211x + 163.56
R2 = 0.9018
14000
IMM (ML/d)
12000
10000
8000
6000
4000
Y
Linear (Y)
2000
0
0
2000
4000
MMD (ML/d)
6000
8000
• Method 2:
Regression of
annual maximum
mean daily flow
series with annual
instantaneous
maximum series of
the same station
Australian Rainfall and Runoff
A guide to flow estimation
INFILLING MISSING RECORDS
•
273 data points from 187 stations were filled by
Method 1
•
60 data points from 44 stations were filled by
Method 2
•
10% of stations did not have any missing
records.
•
Only 7.5 % of data points were infilled.
Australian Rainfall and Runoff
A guide to flow estimation
10
TREND ANALYSIS
Two tests applied, Mann Kendall &
Distribution Free CUSUM Test
• Mann – Kendall test - checks for trends in
time series; and
CUSUM test - examines whether the mean
values in two parts of a record are
different.
Australian Rainfall and Runoff
A guide to flow estimation
TREND ANALYSIS
Mann Kendall test showed 21% of
stations have decreasing trend after
1990s
Vk
Vk - Station 230210
9
8
7
6
5
4
3
2
1
0
1970
Vk
Significant shift
downwards,
after the 1990’s.
1975
1980
1985
1990
1995
2000
2005
Year
Australian Rainfall and Runoff
A guide to flow estimation
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TREND ANALYSIS
It was also useful to plot time series data as
below.
IMM - Station 230210
12000
Flow (ML/d)
10000
Decrease in flows
after 1986
8000
6000
4000
2000
0
1970
1975
1980
1985
1990
1995
2000
2005
Year
This shows 10-15 years of significant
downward trend
Australian Rainfall and Runoff
A guide to flow estimation
TREND ANALYSIS
Conclusions developed were
• Inclusion of sites with short records
questionable
• Cut-off length introduced minimum
record 25 years
• A significant shift from ARR1987 (where
minimum record length of 10 years was
considered).
Australian Rainfall and Runoff
A guide to flow estimation
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RATING CURVE ISSUES
QE = annual maximum flood series data
point (reported value)
QM= maximum measured flow
Rating Ratio ( RR ) =
QE
QM
RR ≈ 1 - considered to be free of rating
curve extrapolation error.
a RR value >> 1 indicates potential rating
curve error
Australian Rainfall and Runoff
A guide to flow estimation
RATING CURVE ISSUES
Graph shows typical example
Likely Rating Curve Error - 222202
6
Data points subject
to possible rating
curve errors
5
QE/QM
4
3
2
1
0
0
10
20
30
40
50
Data Point
Australian Rainfall and Runoff
A guide to flow estimation
13
RATING CURVE ISSUES
• A rating ratio of 20 may be adopted?
• Any station with RR>20 would be
excluded.
Histogram of Rating Ratio Values
10000
4387
Frequency
Frequency
1000
384
90% of rating ratio’s lie between 1 & 20
111
100
61
Rating Ratio - RR
19 18 18
10
9 10 10
4
5
4
5
4
3
2
1
2
1
1
2
2
1
0
0
1
2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50More
Rating Ratio
Australian Rainfall and Runoff
A guide to flow estimation
AT-SITE FLOOD FREQUENCY
• A LP3 distribution was fitted to each
stations annual maximum flood data
• Bayesian parameter fitting procedure
was adopted.
• FLIKE was used.
Australian Rainfall and Runoff
A guide to flow estimation
14
VICTORIA PILOT STUDY
Locations of the study 133 catchments
Australian Rainfall and Runoff
A guide to flow estimation
CATCHMENT AREAS
60
50
Range: 3 – 997 km2
Frequency
40
30
Mean = 319 km2
20
10
0
0 to 50
51 to 100 101 to 200 201 to 500 501 to 750
751 to
1000
Catchment area (km2)
12% catchments < 50 km2,
20% catchments < 100 km2 and
80% catchments < 500 km2.
Australian Rainfall and Runoff
A guide to flow estimation
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STREAMFLOW RECORDS
Frequency
100
80
60
40
20
0
25 to 30
31 to 40
41 to 50
> 51
Record length (years)
Range: 25 to 52 years
Mean: 32 years
Australian Rainfall and Runoff
A guide to flow estimation
CATCHMENT
CHARACTERISTICS
Variable
Description
area
Catchment area (km2)
forest
Fraction of catchment area under forest
Evap
Mean annual areal potential evapotranspiration
Rain
Mean annual rainfall
S1085
Slope of central 75% of main stream
sden
Stream density
I
Design rainfall intensity of 2 and 50 years ARI and 1 and 12 hours
duration
QSA
Fraction quaternary sediment area
Australian Rainfall and Runoff
A guide to flow estimation
16
C10 CONTOUR MAP
Australian Rainfall and Runoff
A guide to flow estimation
C10 REGRESSION EQUATION
C10 = −2.631 − 0.125 log(rain) +
1.02 log(evap) + 0.072 log(S1085)
+ 0.128 log(sden)
rain = mean annual rainfall (mm)
evap = mean annual evaporation (mm)
S1085 = Slope of main stream (m/km)
sden = stream density (km/km2)
Australian Rainfall and Runoff
A guide to flow estimation
17
Q (m3/s)
TESTING Q10 PREDICTION
50
45
40
35
30
25
20
15
10
5
0
Q10_PRM (C10 from
contour map)
Q10_PRM (C10 from
regression)
90% CI-LL
Q10_FFA
T14
T8
T16
T10
T9
3
18
24
36
52
90% CI-UL
Test catchment/ Catchment area
(km 2)
Australian Rainfall and Runoff
A guide to flow estimation
TESTING Q50 PREDICTION
80
70
Q (m3/s)
60
Q50_PRM (C10 from
contour map)
50
40
Q50_PRM (C10 from
regression)
30
90% CI-LL
20
10
Q50_FFA
0
T14
T8
T16
T10
T9
3
18
24
36
52
90% CI-UL
Test catchment/ Catchment area
(km 2)
Australian Rainfall and Runoff
A guide to flow estimation
18
RELATIVE ERRORS
Australian Rainfall and Runoff
A guide to flow estimation
MEDIAN RELATIVE ERROR
ARI
(years)
2
5
10
20
50
100
C10map
28
17
26
30
35
38
C10equation
31
19
23
36
41
44
Australian Rainfall and Runoff
A guide to flow estimation
19
FLOOD FREQUENCY PLOT
Station 227210
100000
Discharge(ML/day)
10000
1000
100
PRM - C10 from contour map
10
1.25
90% confidence limits of LP3
estimate
Quantile - LP3 distribution
Gauged flow
2
PRM- C10 from regression
5
10
20
50
100
200
Annual Exceedance Probability (1 in Y)
Australian Rainfall and Runoff
A guide to flow estimation
QRT PREDICTION EQUATIONS
log( Q ) = b 0 + b1 log( area ) + b 2 log( rain ) + b 3 log( sden ) for T = 2 years
log( Q ) = b 0 + b1 log( area ) + b 2 log( I 2 _ 12 ) + b 3 log( sden ) for T = 5 years
log( Q ) = b 0 + b1 log( area ) + b 2 log( I 2 _ 12 ) + b 3 log( rain ) +
b 4 log( sden ) for T = 10 , 20 , 50 , 100 years
Only 4 variables are required:
area in all equations
sden in all equations
I2_12 for T = 5, 10, 20, 50 and 100 years
rain for T = 2, 10, 20, 50 and 100 years.
Australian Rainfall and Runoff
A guide to flow estimation
20
TESTING Q10 PREDICTION
50
Q (m3/s)
45
40
35
Q10_OLS
30
25
Q10_GLS
20
Q10_FFA
15
90% CI-UL
90% CI-LL
10
5
0
T14
T8
T16
T10
T9
3
18
24
36
52
Test catchment/ Catchment area (km2)
Australian Rainfall and Runoff
A guide to flow estimation
TESTING Q50 PREDICTION
100
Q (m3/s)
90
80
70
Q50_OLS
60
50
Q50_GLS
40
Q50_FFA
30
90% CI-UL
90% CI-LL
20
10
0
T14
T8
T16
T10
T9
3
18
24
36
52
Test catchment/ Catchment area (km 2)
Australian Rainfall and Runoff
A guide to flow estimation
21
RELATIVE ERRORS
Australian Rainfall and Runoff
A guide to flow estimation
FLOOD FREQUENCY PLOT
Australian Rainfall and Runoff
A guide to flow estimation
22
SUMMARY – PILOT STUDY
• The updated PRM can provide design
flood estimates with reasonable
accuracy.
• C10 values can be obtained from
– C10 contour map or
– developed prediction equation (provides
less biased results).
Australian Rainfall and Runoff
A guide to flow estimation
SUMMARY – PILOT STUDY
• Median relative error values for the new
PRM ranged from 17% to 44%. For 7%
cases relative error values > 100%.
• The PRM tends to underestimate flows
compared to flood frequency estimates,
with 60% of the cases being
underestimated.
Australian Rainfall and Runoff
A guide to flow estimation
23
SUMMARY – PILOT STUDY
• Prediction equations have been
developed for Victoria using OLS and
GLS methods.
• Little differences in prediction equations
between OLS and GLS.
• GLS procedure provides better
estimation reliability.
Australian Rainfall and Runoff
A guide to flow estimation
24