## A k i1 2k

or in terms of return period, T,

13.3.3 Fitting frequency distributions

The FEH recommends fitting the GL and GP distributions by the method of L-moments (Hosking and Wallis, 1997). This is the method used in the WINFAP software. WINFAP also provides estimates of the uncertainty in the parameter values for the fitted distributions and confidence limits for the estimated extremes similar to those shown in Table 11.9 and Fig. 11.16. Where a three-parameter distribution is fitted and the k parameter (as defined above for the GEV, GL and GP distributions) is close to zero relative to the estimated standard error, then it is recommended that the equivalent two-parameter distribution (Gumbel, logistic or Pareto) should be used. Pooled growth curves are fitted using pooled L-moment statistics, which are calculated by taking a weighted average of the L-moment ratios of the sites in the pooling group. Longer records are given more weight, as are sites that are most similar to the subject site.

13.4 Example: Flood Estimation Handbook peak flow estimates for the River Brett, Suffolk

The Brett is a tributary of the River Stour in the county of Suffolk in south-east England. The Brett flows though a rural landscape made up of arable land, grassland, and some areas of ancient woodland. The underlying geology is chalk overlain by semi-pervious boulder clay. Soils in the catchment are mixed between freely draining acid loamy soils, and lime-rich loamy clayey soils with slightly impeded drainage. Average annual rainfall for the area is 586 mm.

### 13.4.1 Requirements for flood estimation

Peak flow estimates were required for a location on the River Brett just downstream of the village of Monks Eleigh. The catchment draining to this point has an area of 85 km2 and is as shown in Fig. 13.1. FEH catchment descriptors show that the catchment is moderately impermeable (SPRHOST = 45.7, which is consistent with the soils and land cover) with almost no flow attenuation from lakes or reservoirs expected (FARL = 0.99). FEH methods are considered appropriate because the catchment is larger than the recommended limit of 0.5 km2 and is not heavily urbanised. The proximity of a gauging station at Hadleigh just downstream of the study reach favours the use of the FEH statistical method. The revised (2008) FEH statistical methods are adopted.

Table 13.2 Gauging stations near to the study site on the River Brett

Station name

Drained

Period of record

Suitable for

QMED

estimation?

Suitable for Other comments on station and pooling? flow-data quality

36005 156 1962-2006 Yes-just Yes-good 'Essex'profile (modified

(Hadleigh) acceptable fit at high Flat V Crump) weir with flows low-flow side weir and high-flow rated spillway. Downstream water level recorder to allow for drowning. Naturalised flows from 1962 to 1976. Since 1976, adjustments for artificial influences are no longer made to the gauged daily mean flows. High flows gauged by bridge gauging downstream of the gauging station

36009 26 1968-2006 Yes-good Yes-just 'Essex'profile (modified

(Cockfield) for QMED acceptable Flat V Crump weir). No for pooling spillway. Modular limit of

0.66 m theoretically derived. No telemetry but planned for future. Naturalised flows from 1969 to 1976, only minimal adjustments needed since. High flows measured by cableway gauging upstream of the gauging structure. High flows were calculated or estimated. Also some float-runs

### 13.4.2 Available data

The latest river flow data set available at the time of the study was HiFlows-UK Version 2.2.1 issue of December 2008. Catchment descriptors were obtained from the FEH CD-ROM v3.0 dated 2009. There are two river flow-gauging stations close to the study site (Table 13.2). Station 36005 at Hadleigh is closest to the study site and has a catchment area 1.8 times larger than the study catchment. Station 36009 at Cockfield is also close to the study site. However, this gauge data has been rejected as a donor site for the FEH analysis because it has a poor rating curve compared to the Hadleigh gauge and its catchment is smaller by a factor of 3.3 than the study catchment.

13.4.3 Estimating the median annual maximum flood (QMED)

The FEH empirical formula for estimating QMED from catchment descriptors (13.3) predicts QMED = 8.9m3 s-1. This figure was adjusted using (13.5) and an estimate of

QMED from gauged data at the nearby Hadleigh gauging station to give a final estimate of 8.1 m3 s-1. The close proximity of the catchment gauged by the Hadleigh station to the study catchment (a separation of 3.9 km in terms of catchment centroids) and the very similar physical and climatic characteristics mean that the QMED adjustment increases confidence in the analysis.

ยก3.4.4 Pooled frequency analysis

The pooling group for the study site is shown in the inset map in Fig. 13.1. Stations for pooling are selected based on the similarity of their catchments to the study area. It can be seen that most of the stations selected for pooling are clustered in the same geographic area as the study site. There are four pooling group catchments that are much further away, but which have been selected based on their similar physical characteristics. Analysis of the pooling group includes checks on the suitability of each gauging station. In this case, one station was removed because of significant attenuation from lakes and reservoirs within its catchment area. Another station was highlighted as discordant owing to a large annual maximum (AMAX) flow value that appeared as a statistical outlier. On inspection, this station was retained, as the 'outlying' high flow was believed to be related to accurate gauging of real flood flows.

The final pooling group contains 528 station years of AMAX data. The GL distribution (13.1) fits the data well, with parameter values as follows: 'location' a = 1.00, 'scale' b = 0.264 and 'shape' k = -0.057. The growth curve for the pooling group is shown in figure along with the individual growth curves for each catchment within the group.

Peak-flow estimates for the site follow easily from multiplication of the growth factor Q/QMED for a given return period with the estimated value of QMED. The estimated peak flow for a 100-year return period (1 per cent AEP) is 19.3 m3 s-1, or 2.4 times QMED. The pooling group gauges have record lengths of between 36 and 67 years. Assuming the pooling group is unbiased, the scatter between the background curves in Fig. 13.2 is indicative of the sampling uncertainty associated with the gauged records. For further discussion of the theory and analysis of uncertainty in pooled flood frequency analysis, see Rosbjerg and Madsen (1995), Kjeldsen and Jones (2006) and Kjeldsen et al. (2010).

### 13.4.4.1 Methodology checks

Although the study site has no gauging station, it is good practice to compare the estimated flood frequency curve derived from the pooling group with gauged AMAX flows in the record at Hadleigh. Applying the growth curve to the Hadleigh record would imply that in the 44 years of record, ten gauged annual maxima had return periods of between 2 and 5 years, two had return periods of between 5 and 10 years, three between 10 and 50, and the largest recorded event, in October 1987, would have had an approximate return period of 100 years. These estimates are considered plausible. Specific runoff for the catchment area at the estimated 100-year peak flow is approximately 0.8 mmh-1, which is a plausible value for a relatively permeable catchment with mild slopes and rural land cover.

2 5 10 25 50 100 250 Return period (years)

Fig. 13.2 Pooled dimensionless growth curve for the River Brett study site superimposed on growth curves for individual gauging stations within the pooling group.

13.5 Design event methods in the Flood Estimation Handbook

### 13.5.1 The FEH event models

The original FEH published in 1999 contained an event-based rainfall-runoff model, a modified version of that used in the previous Flood Studies Report of 1975 (Natural Environment Research Council, 1975). It is an example of a model that is based on the concepts of effective rainfall and storm runoff discussed in Section 12.3 and 12.4. It is primarily intended for use at ungauged sites where there is information about rainfalls, but no discharge data available for calibration, particularly in predicting the flood hydrograph that might arise in a catchment for a particular extreme rainstorm event or design storm. The purpose of such a prediction might be in designing a flood runoff detention basin for a new commercial development, or in a dam safety assessment, including the estimation of a probable maximum flood, or for providing the inputs to a flood inundation model for flood risk mapping and planning. The FEH event model essentially combines the calculation of effective rainfall described below in Section 13.5.2, the triangular unit hydrograph described in Section 13.5.4, and a baseflow component.

### 13.5.2 Estimation of a design storm event

The FEH flood hydrograph method is a single event-based rainfall-runoff model. Thus, an important part of the method is the choice of design rain event, as defined in terms of storm duration, total depth and profile, together with the antecedent conditions for the catchment.

Following the FEH recommendations, the storm duration for a particular catchment is defined as:

SAAR\ 1000

where Tp is the estimated time to peak for the catchment, and SAAR is the standard annual average rainfall for the period 1961-90. The total storm depth is estimated using the FEH depth-duration-frequency curves (see Section 9.6.1). Depth-duration-frequency analysis provides standard tools for estimating the total storm volume and duration for different probabilities of exceedance. A complete description of a design storm for use in the event model requires more, however. In particular we will be interested in the average rainfall over a catchment area rather than rainfall at a point, so that the estimated storm depth should be adjusted by an areal reduction factor (see Section 9.4).

We will also require a storm profile, although in the analyses leading to the FEH, the estimated peak discharges were found to be relatively insensitive to the choice of storm profile. Thus, two profiles were suggested for use in design, the 75 per cent winter profile for use in rural catchments and the 50 per cent summer profile for use in urbanised catchments. The percentages refer to the quantiles over all storms analysed, when normalised by storm depth and duration (see Fig. 13.3). These simple profiles have been criticised as too simple, particularly for large catchments with reservoirs where the critical event may be several days long and made up of multiple events; and the Institution of Civil Engineers (1996) has recommended using the profile of the severest sequence of storms of the required duration in the local observed rainfall records.

Finally, the original FEH event model method makes an allowance for the fact that we do not expect a rainfall event of a given probability of exceedance to produce a

flood peak with the same probability of exceedance. This is because of catchment characteristics and antecedent wetness effects. An extreme rainfall on dry ground in a rural catchment in summer might produce a smaller flood peak than a less extreme rainfall falling on a wet catchment in winter. Thus the FEH method makes recommendations about the choice of rainfall return period that will best estimate a flood peak of the required return period (Fig. 13.4).

### 13.5.3 Estimation of percentage runoff

Given a design rainfall, the next stage in the design event method is to estimate the percentage runoff. To do this, FEH provides a method to estimate the standard percentage runoff, which is then modified to reflect particular conditions. The estimation of SPR is based on empirical equations for percentage runoff derived from the analysis of the records from UK catchments up to 500 km2 in area. Once a percentage runoff is defined for a storm, it is applied as a constant proportional multiplier at each time increment of rainfall (see Fig. 12.2b). Note that this will result in a different time distribution of effective rainfall to the $ index approach shown in Fig. 12.2a, even if both can match a required volume of effective rainfall.

The calculation of effective runoff for a rural catchment takes account of the soil characteristics of the catchment, the event rainfall volume and a catchment wetness index effect. It consists of two parts, a SPR and dynamic components (dynamic percentage runoff; DPR) that depend on the antecedent catchment wetness prior to an event (DPRcwi) and the event magnitude (DPRrain). Percentage runoff (PR) for a rural catchment is then calculated as:

The FEH gives a number of ways of determining SPR. When a site is gauged, then SPR can be determined as an average value from an analysis of observed events. A quicker method is provided by a relationship to the BFI, for a catchment that is tabulated for all gauged catchments in the UK. This is:

If an ungauged site is being studied, however, then SPR must be estimated from catchment characteristics. The method for doing so depends on the HOST classification introduced earlier in Section 13.2. Each HOST class is associated with a standard percentage runoff (Table 13.3). The SPR is given by a simple weighted sum over all HOST classes.

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