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The synthesis of design flood hydrographs

Authors:

Abstract

In many instances of flood design especially for flood storage assessment and hydrodynamic modelling, there is a need for a characteristic hydrograph shape as well as a design peak flow. The most common practice is for the use of a unit hydrograph/losses model applied to a design rainfall. In the UK the Flood Studies (FSR) rainfall runoff method is recommended and the method has not been superseded in the Flood Estimation Handbook (FEH). In US and elsewhere the Soil Conservation Service (SCS) method based on similar principles is widely used Both FSR and SCS methods are primarily applicable to small to medium catchments where flow originates as direct runoff from precipitation in the form of rain, uniformly distributed over the catchment. The methods may not be reliable in catchments where floods typically include snowmelt or where runoff is attenuated by surface storages such as lakes and swamps or subsurface storages in karstic limestones or chalk. An upper limit of 1000 km2 is now recommended for the FSR rainfall runoff method. An alternative method (specifically excluding Probable Maximum Flood estimation), applicable in the vicinity of gauged sites is proposed, based on the generalisation of the shape of observed flood hydrographs. Examples are provided for catchments with lake storages and in an Oolitic limestone catchment with a large groundwater component.
2000 D Archer
D Faulkner
J.A. Mawdsley
M. Foster
The synthesis of design flood hydrographs Proceedings of a CIWEM/ICE conference
on Flooding Risks and Reactions, Oct
2000
THE SYNTHESIS OF DESIGN FLOOD HYDROGRAPHS
David Archer, BA, MSc, Dip Hydrol, MCIWEM, Principal Hydrologist
Miranda Foster, BSc, PhD, Hydrologist
Duncan Faulkner, MA, MSc, DIC, Hydrologist
John Mawdsley BSc, PhD, MICE, MCIWEM, Principal Hydrologist,
all Jeremy Benn Associates, Gillow House, Broughton Hall, Skipton, N.
Yorks, BD23 3AN
ABSTRACT
In many instances of flood design especially for flood storage assessment and
hydrodynamic modelling, there is a need for a characteristic hydrograph shape as well as
a design peak flow. The most common practice is for the use of a unit hydrograph/losses
model applied to a design rainfall. In the UK the Flood Studies (FSR) rainfall runoff
method is recommended and the method has not been superseded in the Flood Estimation
Handbook (FEH). In US and elsewhere the Soil Conservation Service (SCS) method
based on similar principles is widely used
Both FSR and SCS methods are primarily applicable to small to medium catchments
where flow originates as direct runoff from precipitation in the form of rain, uniformly
distributed over the catchment. The methods may not be reliable in catchments where
floods typically include snowmelt or where runoff is attenuated by surface storages such
as lakes and swamps or subsurface storages in karstic limestones or chalk. An upper limit
of 1000 km2 is now recommended for the FSR rainfall runoff method.
An alternative method (specifically excluding Probable Maximum Flood estimation),
applicable in the vicinity of gauged sites is proposed, based on the generalisation of the
shape of observed flood hydrographs. Examples are provided for catchments with lake
storages and in an Oolitic limestone catchment with a large groundwater component.
Key Words
Flood alleviation, flood profile, design hydrograph
INTRODUCTION
Many flood studies, especially for the assessment of flood storage and for hydrodynamic
modelling, require a characteristic hydrograph shape as well as a design peak flow. The
shape and the associated volume can have a significant impact on the cost of alleviation
works; any improvement in the reliability of the hydrograph can thus enable a better
balance between the risk of failure of a scheme and the cost of protection. However, flood
hydrograph shape is almost infinitely varied. It depends on four groups of factors:
1. Precipitation amount and distribution in space and time (including snow and
snowmelt);
2. Dynamic properties of the catchment such as soil wetness and land use;
3. Static properties of the catchment such as area and slope;
4. Channel and floodplain morphology, static in the medium time scale.
The static characteristics restrict the range of variation for a particular point on a
catchment but the possible combinations of the dynamic properties ensure a wide range
of behaviour within that range. How then is one to choose a characteristic shape from
within this range?
EXISTING METHODS
Methods in current use throughout the world are usually based on combining the
statistical (or observed) properties of extreme event rainfall for the catchment area with a
black-box or deterministic model of catchment behaviour, in which the dynamic
properties of the catchment are specified in some standard way. The rainfall and loss
function applied determines the flood volume, and the design rainfall and static
catchment characteristics determine the hydrograph shape and associated peak. The result
is a flood hydrograph peak of specified return period and an associated characteristic
hydrograph.
In the US and elsewhere, adaptations of the Soil Conservation Service method using such
principles are in common use(1). In the United Kingdom, the Flood Studies rainfall runoff
method(2) provides the primary basis for defining a design flood hydrograph. The basic
structure of the model has not been superseded with the provision of new statistical
methods in the Flood Estimation Handbook(3), although possible alternatives are
suggested. The FSR design hydrograph is based on:
a design rainfall amount, duration and profile;
a percentage runoff based on static and dynamic characteristics of the
catchment;
a unit hydrograph whose main parameter, time to peak, is derived from
observed flood hydrographs or static catchment and channel characteristics,
and
a baseflow to be added to the flood response hydrograph.
Sutcliffe(4) in introducing the Flood Studies methods gave guidelines for the choice of
flood estimation method and recommended that where a hydrograph shape is required,
the rainfall runoff approach should be applied whether or not flow records exist at the site
The parameters of the catchment model can be obtained from observed rainfall and flow
data using methods defined in IH(5) (1983) and now consolidated in Volume 4 of the
Flood Estimation Handbook (FEH). However several assumptions are independent of
local data or only loosely dependent on them. For example, the rainfall depth or profile
may not be adjusted using local data, apart from on large reservoired catchments.
The original FSR calibration procedure for the method was designed to make a
recommendation of design choices of rainfall return period, storm duration, profile and
antecedent conditions to provide the best match between observed and estimated flood
frequency on average throughout the country. However, a large standard error of estimate
was recognised. In a test of the prediction equations, with respect to the ungauged
situation, 30% of peak flow estimates were outside ± 50%, and 50% of estimates were
outside ± 25%. Subsequent analysis has shown systematic spatial variations in residuals
in comparison to gauged data(6). and a systematic bias in flood growth rates(7). The use of
local data makes some improvement in error bands but the application of the new rainfall
statistics in the Volume 2 of the FEH actually results in some areas in computed flood
growth rates which further diverge from observed growth rates.
With respect to the assessment of peak flow of specified return period, the rainfall runoff
method has been placed at a disadvantage compared to the alternative statistical
procedure (FEH Volume 3), since it has not been updated with the much longer data sets
of river flow now available. The FEH statistical method incorporates these data, and also
takes account of advances in regional frequency estimation techniques, particularly in the
way that data from similar catchments are pooled.
The FEH statistical method is therefore considered to give more reliable estimates of
peak discharge of design return period but does not in itself provide a flood hydrograph.
Where a flood hydrograph is required an alternative or additional approach is needed.
FEH provides three alternatives to reverting directly to the rainfall runoff method.
1. Adjusting the rainfall runoff model parameters, time to peak of the unit hydrograph
(Tp) and standard percentage runoff (SPR) by successive approximation until the
flood frequency curve synthesised by the rainfall runoff method agrees with the curve
synthesised by the statistical method. The design hydrograph is then provided by the
(adjusted) rainfall runoff method. However, in spite of FEH revision of rainfall
estimates, a match cannot be obtained irrespective of the adjustment applied in most
upland areas of UK and elsewhere(7).
2. Calculation of the FSR rainfall runoff flood hydrograph but then rescaling the
ordinates of the hydrograph by the proportion of the statistical method peak to the
rainfall runoff peak, treating baseflow separately.
3. Applying a simplified model of hydrograph shape by computing the hydrograph
width (duration) at 50% of the peak flow either from observed large flood hydrograph
events and taking the median or by means of an equation:
W50% peak = 2.99 Tp(0)0.77 (1)
where Tp(0) is the time to peak of the instantaneous unit hydrograph derived either
from the analysis of flood events or from catchment properties.
An equation is provided for constructing the upper hydrograph from above 50% Qp and
the lower hydrograph is sketched in by hand if required. The resulting flood hydrograph
is symmetrical.
In many instances the flood hydrograph derived by modifications of the rainfall runoff
method may be adequate for design purposes. However, difficulties have been noted or
are foreseen in several categories of catchment.
Very permeable limestone catchments or those with a mixed response(2),(8),(9).
Catchments with very large lakes or sequences of lakes (e.g. Lake District)
Catchments where snowmelt contributes to a significant proportion of extreme flood
events. The rainfall runoff method makes no allowance for snowmelt or rain on snow
events which are generally of longer duration than rainfall-only events.
Sites below a significant tributary inflow with much shorter lag than the main channel
resulting in a double peaked or prolonged hydrograph (e.g. River Spey below Avon
confluence, Lake District Derwent below Cocker confluence)
In spite of the third alternative above suggested by the FEH, it is contended that
inadequate direct use is made of the growing body of gauged hydrograph data in UK
catchments for synthesis of a design hydrograph. Fifteen-minute values of stage and
discharge are available in computer archives for flood events including annual maxima
for 20 or more years for many stations in the UK. Typical flood hydrographs which have
occurred are a better guide to the behaviour of a catchment than those derived by
theoretical or empirical considerations of storm rainfall, amount, duration, seasonality
and profile, unit hydrograph response and baseflow contribution.
The following method is proposed as a means of combining the information from the
flood hydrographs of annual maximum (or peaks over a threshold) floods to derive a
typical observed flood hydrograph shape which can then be scaled with respect to
discharge by reference to peak estimates derived by flood frequency analysis or FEH
methods from catchment properties.
METHOD
1. From each annual maximum flood hydrograph, derive the duration of exceedence
of selected percentiles of peak flow, for example 98%, 95%, 90%, 85%, etc. (Fig. 1).
2. The duration before and after the peak may be assessed to ensure that in synthesis
a more realistic asymmetrical rather than symmetrical profile is derived.
3. For each exceedence percentile, median (or other percentile) durations are derived
and a hydrograph shape which is non-dimensional with respect to discharge is
determined. Mean rather than median duration was also considered but was found that in
the examples considered, individual events of very large duration unduly influenced the
mean value.
4. The median (or other) hydrograph shape can then be applied to the synthesised
peak flow of specified return period derived by flood frequency analysis - if necessary
incorporating both gauged data and pre-gauged historical data.
5. To test the sensitivity of the hydrograph shape to flood magnitude or seasonality,
analysis may be done separately for:
Summer and winter events
Flood events subdivided by rank.
Fig 1 Definition diagram for derivation of duration of exceedence of percentiles of peak
flow.
APPLICATION 1 – RIVER FROME AT EBLEY MILL
The method was applied to the River Frome at Ebley Mill in the Cotswold Hills for
which annual maximum flood hydrographs were available from 1979 to 1996 (19 years).
The catchment of 198.0 km2 is predominantly underlain by highly permeable Oolitic
limestone rocks with very slow runoff response. The lowest 15 to 20% of the catchment
is underlain by much more responsive sandstones (Cotteswold Sandstone and Lias clays).
It is in this portion of the catchment where urbanisation has mainly occurred, Stroud
being the main urban settlement.
Inspection of annual and flood hydrographs indicates that runoff response is dominated
by groundwater, and flood runoff (defined by hydrograph separation of base flow) as a
percentage of storm rainfall averaged 2.4% and did not exceed 8%(10). Some annual
maxima appear to arise solely from a groundwater contribution.
For each annual maximum flood event a tabulation of 15 minute flows was used to
determine the duration before and after each flood peak, above each of the following
percentiles of peak flow - 98, 95, 90, 85, 80, 75, 70, 60, 50, 40, 30, 20, 10%. These are
shown in Tables 1 and 2.
Median durations were then derived for the full set and for subsets based on rank and
seasonality. Floods were divided into three groups according to magnitude (Ranks 1 to 6,
7 to 12, 13 to 19) and medians of these groups derived separately. Only three summer
floods (April to September) occurred in the set. Resulting durations are displayed in Fig.
2. A standard profile based on the Flood Studies rainfall runoff method (without local
adjustment) is also shown for comparison.
Fig. 2 River Frome at Ebley Mill: standardised flood profile, categorised by flood
magnitude and by season. FSR profile is shown for comparison.
The following observations are made on the derived hydrograph shapes:
0
20
40
60
80
100
120
-24 -18 -12 -6 0 6 12 18 24
Hours before and after peak
% of peak flow
Full Set
Rank 1-6
Rank 7-12
Rank 13-19
Summer
Winter
FSR
1. With reference to the median profile for the full set, the importance of
groundwater is shown by the peak being little more than double the initial flow and in
recession by the discharge persisting at over 60% of the peak for nearly 5 days.
2. The profile for the full set and for the Rank 1 to 6 subset differ little. Intermediate
ranked floods are slightly more peaked, though the recession coincides after 12 hours
with the full set. Low annual floods are characterised by a very flat profile and initial
flows over 60% of the peak and levels persisting at nearly 80% of the peak for several
following days.
3. Seasonally subdivided events show significant differences. Summer events (3
only) show much greater peakedness, reflecting both the typically lower starting values of
groundwater discharge and the greater intensity of summer rainfall. Winter events have
higher starting and finishing levels than the full dataset.
4. Although the Flood Studies rainfall runoff method provides a profile which differs
little from the full set profile above 80% of the peak flow, it is otherwise much more
peaked and of shorter duration and volume than the observed median profile. On the
other hand it is less peaked than the median summer profile, although it declines at a
more rapid recession rate to a lower base flow.
5. The similarity of the profile for the full data set of 19 events and for the largest 6
events suggests that the profile from the full set may reasonably be used in design
APPLICATION 2 – RIVER DERWENT AT CAMERTON (LAKE DISTRICT)
The lower River Derwent in the Lake District presents a particular challenge for the
assessment of a design flood hydrograph. The catchment area to the gauging station at
Camerton is 663 km2 of which over 60% is discharged through lakes. This includes
natural lakes with uncontrolled outflow, Bassenthwaite and Derwentwater on the
Derwent, partly controlled flow through Buttermere and Crummock Water on the River
Cocker tributary, and the more significantly controlled flow from Thirlmere Reservoir on
St Johns Beck. The upper part of the catchment consists of grass and heather moorland
draining impermeable lower Palaeozoic rocks and includes the highest rainfall location in
England.
Flood flows undergo considerable attenuation in the lakes, resulting in prolonged outflow
hydrographs. Flood attenuation also results in suppressed flood growth and this is
displayed particularly at the gauging stations at Ouse Bridge (363 km2) below
Bassenthwaite and at Camerton. However the unreservoired lower 40% of the catchment
can occasionally generate significant floods including annual maxima, although rainfall
totals are typically much lower in this reach. Flood hydrographs are often multi-peaked,
resulting either from consecutive bursts of rainfall or consecutive contributions from
different tributaries and reaches. All observed annual maxima are winter events (Oct to
Mar) with 62% occurring from October to December.
To apply the rainfall runoff method requires an estimate of the time to peak of the unit
hydrograph (Tp). The recommended procedure to derive Tp from event unit hydrographs
is very time consuming in the assembly of rainfall and flow data, the selection and
rejection of events, and analysis. In the case of the Derwent, typically non-uniform
distribution of rainfall may result in either rejection of events for analysis or widely
varying Tp between events. Estimation of Tp from catchment descriptors (FEH Vol. 4
Table B1) does not include a lake parameter and is thus unreliable for this catchment.
The alternative FEH method of construction of a design hydrograph based on a
generalised model of hydrograph shape (FEH Vol. 3, Sec. 10) depends also on an
estimate of Tp which is required for Equation 1 to determine the width of the hydrograph
at half the peak flow. It thus also suffers from the extended computation and uncertainty
of the standard FSR rainfall runoff method.
To apply the procedure described above, annual maximum flood hydrographs from 1976
to 1999 for the River Derwent at Camerton were extracted from the EA archive of 15-
minute flows and median and quartile profiles were constructed (Fig. 3) This illustrates
the typically very wide time base but also a significant variation between upper and lower
quartile profiles. The FSR profile based on the assessment of mean lag and time to peak
between rainfall and runoff for observed events on the catchment is shown for
comparison; it has a much narrower time base than the profiles derived from observed
hydrographs.
Fig. 3 River Derwent at Camerton: Median, upper and lower quartile profiles. FSR
profile is included for comparison.
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
-72 -48 -24 0 24 48 72 96 120 144
% of peak flow
M edian
25 %ile
75 %ile
FSR
Variation was investigated further by classifying events within four quartiles of flood
magnitude, in comparison to the median profile (Fig. 4). In common with the Frome at
Ebley Mill, there is a close correspondence between the overall median profile and the
median profile of the upper flow quartile. In contrast the profile for lower quartile flows
is most peaked whilst those in the 25 to 50% flow quartile are most prolonged.
The method again provides a realistic basis, in association with the peak discharge
estimate of the statistical method, of constructing a design flood hydrograph in terms of
discharge and of testing the sensitivity to a range of possible profiles.
Fig. 4 River Derwent at Camerton: Median profiles for different ranges of peak
discharge.
DISCUSSION
A characteristic feature of a hydrograph constructed by standardising on peak flow is the
assumption of proportionality irrespective of peak magnitude. In the case of the Frome at
Ebley Mill, this results in increasing initial discharge with increase in design peak flow
and higher maintained flow after the peak. This concurs with observations of individual
events on this groundwater-dominated catchment, which shows a strong association
between observed annual maxima and initial level.
Over drier catchments in the south and east of England there is typically a stronger
correspondence of annual maximum flood seasonality with periods of low soil moisture
deficit (SMD) than with the season of highest storm rainfall(11). In turn, the association of
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
-48 -24 0 24 48 72 96 120
Hours before and after peak
% of peak flow
Median
>75%ile
<25%ile
50-75%ile
25-50%ile
high baseflow with low SMD supports the contention that on such catchments also, a
baseflow which varies with peak discharge is more appropriate than the invariant base
flow for design events of the FSR rainfall runoff method.
In contrast, it is noted that in the high rainfall regime of the River Derwent at Camerton,
there is no distinct association of initial flow and peak flow. In normalising the
hydrograph on peak flow, this results in the highest peak discharges having the lowest
starting and finishing percentile (Fig. 4, >75%ile) and vice versa for the lowest peak
discharge (<25%ile). This condition does not persist for parts of the hydrograph greater
than 50% of the peak. In this case use of the median flow profile for all design return
periods could result in overestimation of initial discharges for high return periods. It is
suggested that, if it is critical for design, an alternative profile (Fig. 4) could be selected
for initial flow up to 50% of the peak discharge.
CONCLUSIONS
1. Deriving design flow hydrographs from observed floods avoids many of the
complexities and uncertainties associated with rainfall-runoff modelling. The
procedure makes direct use of the available fifteen minute flow data and enables
all flood estimates to benefit from new statistical methods. Analysis is simpler and
quicker than the derivation of Tp from observed events required for the FSR
rainfall runoff method and can be readily carried out on spreadsheet software.
2. Profiles derived from observed flood hydrographs provide a more realistic basis
for generating a design flood hydrograph than standard FSR methods on highly
permeable catchments and those containing significant lake storage. There is no
reason to believe the method would be inferior to FSR methods on catchments
with a more typical response.
3. The method does not require the separate assessment of base flow and storm
runoff but considers the hydrograph in its totality.
4. Flood volumes associated with a flood peak discharge of specified return period
are often much greater than those based on a Flood Studies rainfall runoff profile.
This may have serious implications for the design of flood alleviating storage or
for the return of stored water into the river channel.
REFERENCES
(1) U.S. DEPARTMENT OF AGRICULTURE, SOIL CONSERVATION SERVICE.
National Engineering Handbook, Section 4, Washington DC., 1975
(2) NATURAL ENVIRONMENT RESEARCH COUNCIL Flood Studies Report (5
vols.) NERC, London, 1975
(3) INSTITUTE OF HYDROLOGY. Flood Estimation Handbook (5 vols.) IH,
Wallingford, 1999.
(4) SUTCLIFFE J. V. Choice of estimation techniques. In, Flood Studies conference,
Institution of Civil Engineers, 1975, 67.
(5) INSTITUTE OF HYDROLOGY. Some suggestions for the use of local data in flood
estimation. Flood Studies Supplementary Report, No. 13, 1983.
(6) ARCHER D. R. AND KELWAY, P. S. A computer system for flood estimation and
its use in evaluating the Flood Studies rainfall runoff method. Proc. Instn. Civil Engrs.,
1987, 2 (83), 601.
(7) ARCHER D. R. The Flood Studies Rainfall Runoff method - a fundamental
flaw? Circulation, 1997, 56, 12.
(8) REED, D. W. Engaged on the ungauged: applications of the FSR rainfall-runoff
method. British Hydrological Society, 1st National Symposium, Hull, 1987, 2.1.
(9) GURNELL, A. AND MIDGELEY, P. (1987) Refining the estimation of percentage
runoff in catchments with extreme hydrogeological conditions. British Hydrological
Society, 1st National Symposium, Hull, 1987, 3.1
(10)WALLINGFORD WATER Floodplain mapping - model study of the River Frome
(Gloucestershire), Hydrological Study. Report EX 3171 (For the Environment Agency),
1995.
(11) ARCHER, D. R. (1981) The seasonality of flooding and the assessment of
seasonal flood risk. Proc. Instn. Civil Engrs., 1981, 2 (70), 1023.
Table 1. R. Frome at Ebley Mill. Duration of exceedence of given discharges before the peak for percentiles of peak discharge
(hours).
Year 1979 1993 1995 1983 1992 1990 1984 1986 1994 1988 1981 1987 1982 1989 1985 1980 1997 1991 1996
Flood
Rank
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
Q Peak 19.4 14.9 13.6 13.5 13.5 12.9 12.2 11.9 11.8 11.4 10.9 10.8 10.8 8.1 7.2 6.7 5.6 5.5 4.9
98 % ile 0.5 0.75 0.25 0.5 0.25 2.0 0.25 0.5 0.75 0.75 0.5 1.25 1.0 2.25 4.75 1.5 M 0.5 0.25
95 0.5 2.0 1.0 1.25 2.0 2.25 0.25 0.75 1.75 1.25 1.25 1.75 1.75 2.5 M 2.0 0.25 1.0 3.75
90 1.0 2.5 1.75 2.0 3.25 3.25 0.25 1.25 2.75 1.75 3.75 2.0 2.75 2.75 M 2.75 2.25 4.25 13.7
85 1.25 2.75 2.75 2.5 4.0 4.5 0.25 1.5 3.5 2.0 4.5 2.5 3.5 3.25 M 4.75 6.25 5.5 26.7
80 1.75 3.0 4.25 3.0 4.5 5.25 0.25 2.0 4.25 2.5 4.75 3.0 4.0 4.0 M 6.75 6.5 5.5 39.7
75 2.25 3.25 4.75 3.25 5.25 6.5 0.25 2.25 5.0 2.75 5.0 3.25 4.75 5.0 M 9.5 15.5 5.75 51.7
70 3.0 3.5 5.5 4.0 6.0 43.2 0.25 2.5 6.0 3.25 5.5 3.75 5.25 5.75 M 11.5 15.7 6.5 119.
60 3.75 5.0 47.7 7.75 8.0 44.2 0.5 3.5 48.5 4.5 7.25 4.75 10.0 119. M 134. 40.2 7.5 >200
50 4.0 6.0 91.2 8.0 11.0 88.7 0.5 4.25 85.7 7.0 12.2 6.25 >200 153. M >195 64.5 13.2
40 4.5 26.5 191. 8.5 55.5 125. 1.0 185. 133. >180 38.5 7.75 >190 M >200 21.0
30 6.0 84.0 >200 20.0 119. >190 1.0 >200 >200 48.7 17.7 74.0
20 14.5 94.0 >200 >170 1.25 >200 >200 >200
10 >200 >200 24.0
Table 2. River Frome at Ebley Mill. Duration of exceedence of given discharges after the peak for percentiles of peak discharge
(hours).
Year 1979 1993 1995 1983 1992 1990 1984 1986 1994 1988 1981 1987 1982 1989 1985 1980 1997 1991 1996
Flood
Rank
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
Q Peak 19.4 14.9 13.6 13.5 13.5 12.9 12.2 11.9 11.8 11.4 10.9 10.8 10.8 8.1 7.2 6.7 5.6 5.5 4.9
98 % ile 0.5 0.5 0.5 0.5 0.25 1.25 0.0 0.5 0.5 0.75 0.25 0.75 1.25 2.5 7.75 4.25 M 0.0 0.25
95 0.75 1.0 1.5 1.0 1.75 2.25 0.25 1.0 1.25 1.75 0.75 1.25 2.0 3.5 36.5 5.25 0.25 0.0 1.75
90 1.5 1.5 3.5 2.25 2.5 4.0 0.25 1.75 3.25 2.75 1.25 2.0 2.75 5.25 61.5 6.25 3.75 1.0 2.75
85 2.0 2.0 4.5 3.25 3.75 7.0 0.5 2.75 4.25 3.75 1.75 2.5 4.0 7.5 301. 9.75 5.75 2.25 3.0
80 2.5 2.5 6.5 4.25 5.25 17.5 0.5 3.75 5.25 4.5 2.5 3.25 5.25 11.2 >400 79.0 7.5 3.25 187.
75 3.0 3.0 10.0 7.5 7.0 41.5 0.5 5.25 47.5 5.25 3.75 4.0 6.75 16.5 103. >250 4.0 222.
70 3.5 3.5 44.0 10.0 9.25 69.2 0.75 7.25 72.0 7.0 6.5 5.25 11.2 55.2 127. 5.0 296.
60 4.75 6.0 120. 61.0 69.7 311. 1.0 16.2 325. 204. 168. 6.75 24.5 140. 234. 6.5 >400
50 6.75 86.0 176. 92.0 128. >400 1.75 294. >400 371. 301. 12.7 192. 252. >400 13.0
40 11.2 374 >400 188. 200. 2.5 >400 >400 >400 143. 336. >400 298.
30 120. >400 >200 >400 4.25 336. >400 >400
20 >300 6.75 >400
10 40.0
... Amongst earlier works on the methods of deriving DFHs applicable to catchments having a paucity of precipitation data that could be related to the methods proposed in this study were the typical hydrograph (TH) method (e.g. Nezhikhovsky 1971, Sokolov et al. 1976, Robson and Reed 1999, Archer et al. 2000, Merleau et al. 2007, Sauquet et al. 2008, Xiao et al. 2009, Mediero et al. 2010, Paquet 2019) and the statistical methods (e.g. Gray 1961, Ciepielowski 1987, Yue et al. 2002, Pramanik et al. 2010, Serinaldi and Grimaldi 2011, Brunner et al. 2017, Koutsoyiannis 2019, these two methods being amongst the four (the other two being the TUH and SUH) into which all methods of producing DFH were categorized by Yue et al. (2002). ...
... Here the term percentile, rather than percent, is used to refer to a fraction of the peak flow of a flood hydrograph, in the light of "the assumption of proportionality irrespective of peak magnitude" (Archer et al. 2000) in "standardising [the flood hydrographs] on peak flow," by noting that (a) different flood hydrographs recorded at a gauging site would have different magnitudes of peak flow, and (b) the subjective assessment of similarity of the recorded flood hydrographs would be convenient from the widths of exceedance of the hydrographs at selected fractions -for example, at three-fourths, i.e. the 75th percentile, at half, i.e. the 50th percentile, and so on -of the respective peak flows. ...
... Figure 3 shows examples of standardized flood hydrographs at Station no. 7009 for the flood events presented in Fig. 2. The nonparametric median hydrograph (Archer et al. 2000) derived from 30 standardized flood hydrographs at this station is also plotted in Fig. 3. ...
Article
A paucity of precipitation data often precludes the application of traditional unit hydrograph and synthetic unit hydrograph methods for generating the design flood hydrograph (DFH) at a catchment outlet. However, flow data, either recorded or derived by deterministic approaches, are readily obtained for many catchments. In this paper, analytical methods for generating a DFH having its peak matching the peak flow of a specified return period, or a flood hydrograph beneath a known peak flow at a site, are presented. Only flow data in the case of a gauged site, and flow data together with data of physical descriptors of catchments at gauged sites in the vicinity in the case of an ungauged site, are used to develop a parametric semi-dimensionless characteristic flood hydrograph (CFH); finally, the CFH, which also enables volume estimation, is scaled up for fleshing out a DFH beneath a specified peak flow at that site.
... Flood frequencies with 0.02, 0.01, 0.005, and 0.002 exceedance probabilities (50, 100, 200, and 500 return year periods, respectively) were estimated by fitting the Log-Pearson Type III distribution. For a given location, the timing structure dictating the shape of flood events was estimated from flood simulation or historical records following a methodology proposed by Archer (2000) [27]. The synthetic hydrograph of flood events of desired return periods was constructed by combining the timing structure and flood magnitude from the FFA. ...
... Flood frequencies with 0.02, 0.01, 0.005, and 0.002 exceedance probabilities (50, 100, 200, and 500 return year periods, respectively) were estimated by fitting the Log-Pearson Type III distribution. For a given location, the timing structure dictating the shape of flood events was estimated from flood simulation or historical records following a methodology proposed by Archer (2000) [27]. The synthetic hydrograph of flood events of desired return periods was constructed by combining the timing structure and flood magnitude from the FFA. ...
... Construction of appropriate synthetic design hydrographs (SDH) is an old topic (e.g., Snyder 1938) that has been revisited over the time by applying several different approaches (Sokolov et al., 1976;Yue et al. 2002; Serinaldi and Grimaldi 2011 among others) [29][30][31][32]. In this work, we adopted a procedure described in Archer et al. (2000), which is, in fact, similar to the typical hydrograph method (Sokolov et al. 1976) but utilizes information from more than just a single hydrograph for the construction of SDH [27]. A similar approach for defining the shape of SDH was also followed by Sauquet et al., (2008) [33]. ...
Article
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Worldwide, many river floodplains contain critical infrastructure that is vulnerable to extreme hydrologic events. These structures are designed based on flood frequency analysis aimed at quantifying the magnitude and recurrence of the extreme events. This research topic focuses on estimating flood vulnerability at ungauged locations based on an integrative framework consisting of a distributed rainfall-runoff model forced with long-term (37 years) reanalysis meteorological data and a hydraulic model driven by high-resolution airborne LiDAR-derived terrain elevation data. The framework is applied to a critical power infrastructure located within Connecticut's Naugatuck River Basin. The hydrologic model reanalysis is used to derive 50-, 100-, 200-, and 500-year return period flood peaks, which are then used to drive Hydrologic Engineering Center's River Analysis System (HEC-RAS) hydraulic simulations to estimate the inundation risk at the infrastructure location under different operation strategies of an upstream reservoir. This study illustrates the framework's potential for creating flood maps at ungauged locations and demonstrates the effects of different water management scenarios on the flood risk of the downstream infrastructure.
... Flood frequencies with 0.02, 0.01, 0.005, and 0.002 exceedance probabilities (50, 100, 200, and 500 return year periods, respectively) were estimated by fitting the Pearson Type III distribution. These peak flows were then used to construct synthetic hydrographs using a methodology proposed by Archer (2000). Based on LIDAR derived high resolution DEM, these synthetic hydrographs forced HEC-RAS to generate flood inundation maps in a region controlled by a dam. ...
... Finally, the sensitivity of the design hydrograph shape was tested in regards to flood magnitude. For full explanation of the method, review the "Methods" section in Archer et al. (2000). This method was used to construct synthetic hydrographs for flood events at 50, 100, 200, and 500-yr return periods used as upstream boundary conditions in river reach "A" for HEC-RAS modeling. ...
... Snowmelt is a crucial contributor to flooding in the Naugatuck River basin. This study instead uses an alternative Synthetic Hydrograph method proposed byArcher et al. (2000). Archer et al. compare their method against FSR rainfall runoff method in two basins and find that the analysis is simpler and quicker. ...
Article
In the United States, many river floodplains contain critical infrastructure that is vulnerable to extreme hydrologic events. These structures are designed based on flood frequency analysis aimed at quantifying the magnitude of the extreme events. However, many floodplains are ungauged or poorly gauged, making flood frequency analysis significantly uncertain. This research topic focuses on estimating flood frequency peaks for an ungauged critical infrastructure within Connecticut’s Naugatuck River Basin utilizing a physically based approach consisting of a distributed rainfall-runoff model forced by long-term reanalysis meteorological data and a hydraulic model driven by high-resolution LiDAR derived terrain elevation data. The hydrologic model reanalysis is used to derive 50-, 100-, 200-, and 500-year return period flood peaks, which are then used to drive one-dimensional HEC-RAS unsteady hydraulic model to estimate the inundation risk of a sub-station and evaluate hydraulic structure operation strategies to reduce inundation risk of the downstream infrastructure. This study illustrates the potential of the physically based approach to creating flood maps in an ungauged basin and demonstrates the effects of different water management scenarios on the flood risk of the downstream infrastructure.
... It is made possible thanks to the Archer's method of determining nonparametric hydrograph (i.e., the median of recorded hydrographs). The nonparametric hydrograph determined by the Archer's method is used only to determine the value of hydrograph width at 50% (W50) and 75% (W75) of peak flow and the skewness coefficient s (Archer et al. 2000). The Archer's method uses W50 and W75 similarly to the Snyder method (1938) where with similar parameters characterizing the Synthetic Unit Hydrograph (Snyder 1938;Challa 1997). ...
... This hydrograph represents the median durations of a given percent flow independently for rising and falling limbs. It is used to determine the value of the hydrograph width at 50% (W50) and 75% (W75) of peak flow and the skewness coefficient s (Archer et al. 2000). The parameters are used to determine the shape of a parametric hydrograph from W50 to peak flow. ...
Article
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The gamma distribution functions with one shape parameter, employed to describe the parametric hydrograph, proved ineffective for the upper Vistula River and the middle Oder River water regions. It was therefore necessary to find a different function. The Pearson Type IV distribution functions proposed by Strupczewski with one and two shape parameters were analyzed for their applicability based on the data acquired from 60 water gauges, 30 of which were located on the Vistula River and the other 30 were on the Oder River. The shape parameter (parameters) and the time of rising limb were optimized based on the calculated hydrograph widths at 50% and 75% of peak flow (W50 and W75) as well as on the skewness coefficient s. The calculated parametric hydrographs were compared with the nonparametric input hydrographs with regard to the closeness of their volumes and the position of their centers of gravity. Both Pearson Type IV distribution functions proved to fit well. However, the function with two shape parameters did not yield the exact solution since the condition of the assumed objective function was met by a very large group of pairs of m and n shape parameters. It was therefore assumed that the recommended function is the Pearson Type IV distribution with one shape parameter. This function has an additional advantage of having an inflection point located between the W50 and W75, which allows to use the exponential function for the rising or recession limb that better describes either part of the hydrograph.
... Parametric hydrographs require that their course be a functional description of nonparameteric hydrographs. The methods used in Poland to determine nonparametric hydrographs are the Warsaw University of Technology method (Gądek, Środula 2014) and the Cracow method (Gądek, Tokarczyk 2015), in which hydrographs are determined by flow for a given time, and the Archer method using time averaging (Archer et al 2000). The Warsaw University of Technology method and the Cracow method may be, after some modifications, adjusted to the rules of Archer's nonparametric hydrograph description (Gądek et al 2017). ...
... Archer (Archer et al 2000) developed a method of constructing nonparametric hydrographs, which belongs to a group of issues referred as "designed hydrology". Fig. 1 presents a hydrograph constructed by this method on the basis of the four biggest registered flood waves. ...
Article
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Nonparametric hydrographs, constructed by the method suggested by Archer, are usually used for developing parametric design hydrographs. Flow changes in time are described by the UPO ERR Gamma complex function, which denotes a Gamma curve reformulated to have a Unit Peak at the Origin (abbreviated to UPO), supplemented by the Exponential Replacement Recession (ERR) curve. It may be observed, that this solution does not work in some areas of the upper Vistula and middle Odra catchments when the times of the rising limb of a hydrograph are higher than the times of the falling limb, i.e. when the skewness coefficient approximates 0.5 or higher values. Better results can be achieved with the function suggested by Strupczewski in 1964. It is a solution which uses two parameters of the flood hydrograph. The objective of the present paper is to assess the Strupczewski method by comparing it with a complex UPO ERR Gamma function for gauged cross-sections in the upper Vistula and middle Odra catchments. The assessment was carried out for 30 gauged cross-sections (15 in each river catchment). The parameters were optimized for width-hydrograph descriptors W75 and W50, designed by the Archer method, and for the skewness coefficient s. Optimization using only two width-hydrograph descriptors aims to test how the Strupczewski metho works for cross-sections for which the values of width-hydrograph descriptors W75 and W50 are known. The assessment of both methods was carried out with reference to a nonparametric hydrograph constructed by the Archer method. The results of these assessments suggest that the Strupczewski method may be used not only for gauged cross-sections, but also for ungauged ones.
... Parametric hydrographs require that their course be a functional description of nonparameteric hydrographs. The methods used in Poland to determine nonparametric hydrographs are the Warsaw University of Technology method (Gądek, Środula 2014) and the Cracow method (Gądek, Tokarczyk 2015), in which hydrographs are determined by flow for a given time, and the Archer method using time averaging (Archer et al 2000). The Warsaw University of Technology method and the Cracow method may be, after some modifications, adjusted to the rules of Archer's nonparametric hydrograph description (Gądek et al 2017). ...
... Archer (Archer et al 2000) developed a method of constructing nonparametric hydrographs, which belongs to a group of issues referred as "designed hydrology". Fig. 1 presents a hydrograph constructed by this method on the basis of the four biggest registered flood waves. ...
Article
Full-text available
Nonparametric hydrographs, constructed by the method suggested by Archer, are usually used for developing parametric design hydrographs. Flow changes in time are described by the UPO ERR Gamma complex function, which denotes a Gamma curve reformulated to have a Unit Peak at the Origin (abbreviated to UPO), supplemented by the Exponential Replacement Recession (ERR) curve. It may be observed, that this solution does not work in some areas of the upper Vistula and middle Odra catchments when the times of the rising limb of a hydrograph are higher than the times of the falling limb, i.e. when the skewness coefficient approximates 0.5 or higher values. Better results can be achieved with the function suggested by Strupczewski in 1964. It is a solution which uses two parameters of the flood hydrograph. The objective of the present paper is to assess the Strupczewski method by comparing it with a complex UPO ERR Gamma function for gauged cross-sections in the upper Vistula and middle Odra catchments. The assessment was carried out for 30 gauged cross-sections (15 in each river catchment). The parameters were optimized for width-hydrograph descriptors W75 and W50, designed by the Archer method, and for the skewness coefficient s. Optimization using only two width-hydrograph descriptors aims to test how the Strupczewski method works for cross-sections for which the values of width-hydrograph descriptors W75 and W50 are known. The assessment of both methods was carried out with reference to a nonparametric hydrograph constructed by the Archer method. The results of these assessments suggest that the Strupczewski method may be used not only for gauged cross-sections, but also for ungauged ones.
... A parametric flood hydrograph is understood as one or two equations describing a nonparametric hydrograph. The methods used for the construction of nonparametric hydrographs comprise methods developed by the Warsaw University of Technology (Gądek 2012), Hydroproject (Gądek, Środula 2014) and the Cracow method (Cracow University of Technology) (Gądek, Tokarczyk 2015), in which hydrographs are constructed using a traditional scheme regarding the flow, and the Archer method using averaging by time (Archer et al. 2000). Parametric hydrographs are constructed using equations developed by: Strupczewski (1964), Baptista and Michel (1990), McEnroe (1992), Ciepielowski (2001) and also parabolic functions (Reed, Marshall 1999) using Gamma distribution, Inverse Gaussian, and Negative Binominal curve (O'Connor et al. 2014), Weibull andHayashi curve (1986). ...
... A nonparametric hydrograph construction method after Archer (Archer et al. 2000) belongs to a group of topics defined as "new hydrology". Figure 1 shows a hydrograph constructed with this method. ...
Article
Full-text available
The Archer method for construction of nonparametric hydrographs was regarded as the basic one for constructing design hydrographs in gauged cross sections. The hydrographs designed using this method belong to a group of non-formalized hydrology. Unlike the commonly used formalized methods, where a nonparametric hydrograph is strictly determined and defined, the hydrographs defined in this way are constructed on the assumption, that flow is the main determined parameter. On the other hand, the Archer method assumes that the basic parameter is time, which is determined for assigned standardized flow, called a flow percentile. Hydrographs constructed using this method are the basis for constructing parametric design hydrographs used for engineering computations. The Archer method is relatively new and should be verified for various regions. Presented manuscript compares the results obtained using this method in the middle Odra and upper Vistula basins with the nonparametric method developed at the Cracow University of Technology, called the Cracow method. The obtained results show, that four highest registered flood waves are sufficient to construct a nonparametric design hydrograph, whereas semi-standardized volumes above descriptors W75 and W50 and the duration time of the descriptors are bigger than the volumes and duration times calculated by means of the Cracow method in the Vistula River basin, and approximate with regard to the values in the Odra River basin.
... Consequently, calibration of ReFH2 and previous UK rainfall-runoff methods (FSR, FEH, and ReFH) has focused on how well they reproduce flood-frequency relationships at gauged sites, using the gauged data alone for shorter return periods, or in a regional analysis with heavy at-site weighting for longer return periods. Neither ReFH2 nor any previous UK rainfall-runoff method has been extensively evaluated in terms of simulated event hydrograph, and therefore simulated runoff volume, the most comprehensive study as of 2019 being an evaluation of the ReFH2 design hydrograph shape against the empirical median hydrograph (Archer, Foster, Faulkner, & Mawdsley, 2000) for 20 small catchments up to 40 km 2 (Environment Agency, 2012). Evaluating performance in terms of runoff volume is difficult, as it is often not possible to calculate a closed water balance over an observed event; further rainfall may occur before flows have receded to pre-event levels, and it may not be clear that flows at the start of an event would have followed a pattern of recession in the absence of rainfall. ...
Article
Full-text available
Standard flood risk estimation methods in the United Kingdom have largely focused on peak flows at ungauged locations. However, the importance of whole‐hydrograph and event volume estimation in a design context is increasing with the application of unsteady‐state hydraulic models and construction of sustainable drainage systems. Here, we explore the relationship between peak flow estimation accuracy and flood volume estimation accuracy across 780 events in 81 catchments. Runoff hydrographs are modelled using ReFH2, a rainfall‐runoff model widely used by practitioners for design flood estimation in the UK. We find that strong performance in peak flow estimation is highly correlated with strong performance in event volume estimation, and that between‐event variation in performance is greater than the typical reduction in performance when moving from calibrated to design (regression‐based) model parameters. Unfortunately, evaluating model performance in terms of runoff volume is complicated by the fact that measured rainfall hyetographs and runoff hydrographs are themselves estimates that can disagree with each other for legitimate reasons. We demonstrate that it is not always possible, expected or realistic to close the water balance over an event in a topographically defined river catchment. Hence, ‘errors’ in modelled hydrographs cannot be solely attributed to modelling deficiencies.
... Originating from lumped hydrological models, the linear reservoir routing (LRR) can also been extended to distributed hydrological models with promising efficiency and acceptable accuracy, such as the parallel linear reservoir (PLR) (Archer et al., 2000) and fully distributed linear reservoir (FDLRR) (Shen et al., 2016). ...
Article
Snow processes in mid- and north-latitude basins and their interaction with runoff generation at hyperresolution (< 1km and <hourly) pose challenges in current state-of-the-art distributed hydrological models. These models run typically at macro to moderate scales (>5 km), representing land surface processes based on simplified couplings of snow thermal physics and the water cycle in the soil-vegetation-atmosphere (SVA) layers. This paper evaluates a new hydrological model capable of simulating river flows for a range of basin scales (100 km² to >10,000 km²), and a particular focus on mid- and north-latitude regions. The new model combines the runoff generation and fully distributed routing framework of the Coupled Routing and Excess STorage (CREST) model with a new land surface process model that strictly couples water and energy balances at the SVA layer, imposing closed energy balance solutions. The model is vectorized and parallelized to achieve long-term (>30 years) high-resolution (30 m to 500 m and subhourly) simulations of large river basins utilizing high-performance computing. The model is tested in the Connecticut River basin (20,000 km²), where flooding is frequently associated with interactions of snowmelt triggered by rainfall events. Model simulations of distributed evapotranspiration (ET) and snow water equivalence (SWE) at daily time step are shown to match accurately ET estimates from MODIS (average NSCE and bias are 0.77 and 6.79 %) and SWE estimates from SNODAS (average correlation and normalized root mean square error are 0.94 and of 19%); the modeled daily river flow simulations exhibit an NSCE of 0.58 against USGS streamflow observations.
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Using data from 520 gauging stations in Britain and gridded rainfall datasets, the seasonality of storm rainfall and flood runoff is compared and mapped. Annual maximum (AMAX) daily rainfall occurs predominantly in summer, but AMAX floods occur most frequently in winter. Seasonal occurrences of annual daily rainfall and flood maxima differ by more than 50% in dry lowland catchments. The differences diminish with increasing catchment wetness, increase with rainfalls shorter than daily duration and are shown to depend primarily on catchment wetness, as illustrated by variations in mean annual rainfall. Over the whole dataset, only 34% of AMAX daily flood events are matched to daily rainfall annual maxima (and only 20% for 6-hour rainfall maxima). The discontinuity between rainfall maxima and flooding is explained by the consideration of coincident soil moisture storage. The results have serious implications for rainfall-runoff methods of flood risk estimation in the UK where estimation is based on a depth–duration–frequency model of rainfall highly biased to summer. It is concluded that inadequate treatment of the seasonality of rainfall and soil moisture seriously reduces the reliability of event-based flood estimation in Britain.
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