Contrasting seasonality of storm rainfall and ﬂ ood runoff in the UK and some implications for rainfall-runoff methods of ﬂ ood estimation

Using data from 520 gauging stations in Britain and gridded rainfall datasets, the seasonality of storm rainfall and ﬂ ood runoff is compared and mapped. Annual maximum (AMAX) daily rainfall occurs predominantly in summer, but AMAX ﬂ oods occur most frequently in winter. Seasonal occurrences of annual daily rainfall and ﬂ ood 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 ﬂ ood events are matched to daily rainfall annual maxima (and only 20% for 6-hour rainfall maxima). The discontinuity between rainfall maxima and ﬂ ooding is explained by the consideration of coincident soil moisture storage. The results have serious implications for rainfall-runoff methods of ﬂ ood 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 ﬂ ood estimation in Britain.


INTRODUCTION
Seasonality is an obvious feature of most global climates and is demonstrated in seasonal variations in extreme rainfall and flood occurrence. In Britain, long-duration frontal rainfall and occasional snow dominate in winter, while convective storms in summer increase the frequency and intensity of short-period rainfall. This seasonality is intensified by higher temperatures and evaporation in summer compared with winter, with resulting seasonal variation in soil moisture status at the onset of storm rainfall.
An early illustration of the contrast in the seasonality of storm rainfall is provided by the Flood Studies Report (FSR) (NERC ) which showed how monthly and seasonal maximum rainfall compare as a percentage of annual maxima in Britain. Seasons were defined as 'summer' (six months: May-October) and 'winter' (six months: November-April) (Volume II, Meteorological Studies Table 3.9). The contrast between summer and winter rainfall was shown to be greatest in areas of low average annual rainfall (standard average annual rainfall (SAAR) 500-600 mm) compared with wetter areas (SAAR >2,000 mm) and was much stronger at short durations (1 hour) compared with durations of 1 day or more. Dales & Reed () found that the mean date of occurrence of annual maxima daily rainfall ranged from mid-August in eastern and central England to late October in SW England. Jakob () studied the average occurrence date of 1-day POT (peaksover-threshold) rainfall extremes and showed that in Scotland and Wales, most events occur during late autumn and winter, whereas in most of England the average date is in summer and early autumn. Wales using 30 years of gauged river-flow records . Flooding occurred earlier in small catchments draining higher elevations in north and mid-west Wales.
Low altitude regions in West Wales experienced flooding during October-January, while large eastern-draining catchments experienced later flooding (January-February).
The mismatch between the seasonal timing of extreme rainfall and extreme flood runoff in Britain has been known and investigated for several decades. Archer (), using gauged flow data from 46 catchments in northeast England, showed that monthly maximum daily rainfall peaked in summer but never coincided with the seasonality of monthly flood runoff which peaked in autumn in upland catchments and in January in dry lowland catchments. The seasonality of flood runoff was observed to be more closely associated with the seasonality of soil moisture deficit than with that of rainfall maxima. In an example lowland catchment (Skerne at Bradbury), the month of maximum daily rainfall (July) had not a single flood >0.25 year return period in a 21-year record. Cunderlik & Burn () noted that catchments that exhibit a weak relationship between extreme rainfall and flood timing are mainly due to more frequent periods of soil moisture deficit and higher catchment permeability. Webster () also examined the relationship between rainfall frequency and flood frequency and also noted the effects of catchment wetness and soil characteristics and particular problems in permeable catchments.
Seasonality is an important property with respect to flood risk estimation but its effects are usually considered with respect to statistical methods which have two key com- Seasonality, and the mismatch between the seasonal occurrence of storm rainfall and flood flows, also has serious practical consequences for those methods of flood risk estimation that rely on annual statistics of storm rainfall amount, duration and time distribution. The rainfall-runoff (RR) method of flood estimation is one of two recommended for general use in the UK (Institute of Hydrology ).
Some effects of the seasonality of storm rainfall and runoff are identified explicitly in recent versions of the method, but we contend that the full implications of seasonality have not yet been appreciated. The role of seasonality in successive versions of the RR method is reviewed below.
Seasonality and flood risk estimation using UK RR models The RR method of flood estimation was developed as part of the FSR (NERC ). It has gone through several revisions in the FEH (Institute of Hydrology ), in Kjeldsen et al.
() ('revitalisation') and in Stewart et al. (). Although details have changed, the basic philosophy of the method remains the same. While a specific peak discharge may be produced from an infinite number of combinations of rainfall properties and antecedent catchment wetness, the object of the RR method is to reduce this variety to manageable proportions. The FSR RR method was based on the results of a simulation study to provide criteria for the selection of combinations of antecedent moisture condition and the return period of design rainfall to produce flood hydrographs with a specified return period. Although more complex in design and implementation than the alternative statistical method, it has the advantage of providing a full design hydrograph along with a peak discharge of given annual probability. The effects of the seasonality of storm rainfall and runoff are identified explicitly not only in recent versions of the method (i.e. the ReFH method) but also implicitly in these and earlier versions.
At the core of the FSR and subsequent RR methods is the provision of a depth-duration-frequency (DDF) model of all year rainfall mapped over the country. The FSR version used an interpolation between 2-day and 60minute rainfall to provide estimates of rainfall of the given return period and duration for locations throughout the country. No explicit allowance was made for differences in seasonal rainfall magnitude but, given the dominance of intense short-period rainfall in summer, the annual series is strongly biased towards summer rainfall, especially at durations of less than 1 day. In addition, for individual catchments there was no explicit allowance for differences between summer and winter in initial catchment wetness as expressed through a Catchment Wetness Index (CWI); the design percentage runoff between events of different return periods only varied with the design storm precipitation. The CWI does vary between catchments with SAAR but even here it varies minimally for catchments with an annual rainfall >850 mm and is biased towards winter conditions. The FSR RR method provided alternative seasonal design storm profiles for summer and winter but for the majority of catchments with urban and suburban land cover with urban extent (URBEXT) <0.125, the winter profile was recommended as 'on predominantly rural catchments floods normally occur in winter'. Hence, flood estimation was based on a rainfall magnitude biased towards summer, winter antecedent conditions and a winter storm profile.
As shown below summer-based annual maximum (AMAX) rainfall only rarely leads to an AMAX flood. The FSR implicit means of accounting for the mismatch of rainfall and flood occurrence was through inequality of the rainfall return period and the peak flow return period.
Thus, an 81-year return period storm rainfall was specified to result in a flood peak return period of 50 years. This may have been a logical way of dealing with the mismatch of rainfall biased towards summer and flow biased towards winter. However, there was no corresponding means of providing an upward bias in the return period between lower rainfall in winter and the higher flow return period, such as was noted by Webster ().
The FEH adopted the general principles of the FSR model but developed a new rainfall DDF model based on a much larger dataset than had been available for FSR (Institute of Hydrology ). It adopted a 2-year rainfall depth (RMED) rather than the 5-year rainfall of FSR as the index variable but again with respect to annual maxima rather than subdivided by season. That summer rainfall events dominate in determining the all-year growth curve was acknowledged. The procedure continued to apply a scaling factor to allow unequal rainfall and flow return periods as the FSR and to use the same basis for the application of winter or summer rainfall profiles. The longer datasets permitted more flexible regionalisation.
However, Babtie () found that estimates for 150 years 1-hour rainfall were substantially higher in the FEH than in the FSR, except for parts of eastern Scotland; estimates were more than 50% greater in many upland areas in the west and in much of eastern England. Estimates of T-year flood magnitudes were generally found to be higher than FSR estimates ( As a result, a revitalisation of the FSR/FEH model was initiated, referred to as ReFH. It specifically recognised problems arising from the combination of design storm rainfall mainly in summer and typical winter soil wetness. However, the design rainfall continued to use the DDF model developed for FEH using annual (rather than seasonal) maximum rainfall (Faulkner ). ReFH then used a 'seasonal correction factor' as a multiplier of annual rainfall to determine a seasonal design rainfall depth. This factor was derived by fitting a ratio between annual and seasonal maxima for daily and sub-daily rain gauges (mainly in central England) against annual rainfall (SAAR) for a range of durations and for each season. For the winter season, it was modelled using an exponential distribution (ReFH Appendix G), but it is noted that the graphical relationship shows a very wide spread of points, with progressively increasing spread for durations of less than one day and for catchments with SAAR less than 1,000 mm.
For a given catchment, separate seasonal estimates are not recommended but, as in previous versions, catchments were allocated to winter or summer seasons on the basis of the predominant season of flooding, winter for rural catchments and summer for urban catchments.
The ReFH design method was calibrated to ensure that flood frequency curves derived from the method correspond with those derived from the FEH statistical method. The inequality between rainfall growth curves and flow growth curves derived from a pooled analysis of AMAX series was perceived as a problem; the rainfall growth curves were steeper. This implied that rainfall inputs must be reduced by a greater amount at high return periods than at low return periods. The FSR/FEH solution of using a scaling factor between rainfall and a flow return period was thus abandoned in favour of an equal relationship, 'in order to increase transparency'. Instead, an adjustment (α parameter) was introduced as a multiplier for the initial soil moisture condition (C ini ) to ensure that the design rainfall of a given return period translates to the same return period flow by reducing runoff production as return period increases. Although Kjeldsen et al. () state that the parameter α 'does not have a direct physical interpretation,' it seems clearly related to seasonality and the design values were specified separately for winter (rural) catchments and summer (predominantly urban) catchments. In both cases, the effect of α is to reduce runoff production as the rainfall return period increases but by a larger amount on summer catchments. Subsequent versions of RefH (ReFH2 onwards) developed an approach for estimating C ini that did not require the alpha factor through the use of an alternative C ini model.
As the estimates by the ReFH method were designed to correspond with FEH statistical estimates rather than observed flood frequencies, it lost some of its value as an independent flood peak estimation method and possibly incorporated some of the bias and uncertainty associated with the statistical method. Its main advantage then was in providing a flood hydrograph of the specified return period.
In response to concerns, expressed by reservoir engineers, about the apparently high flood estimates when applied to very high return periods, a revision of the FEH DDF model was commissioned by Defra (Stewart et al. ). The main focus of the report was to develop a new statistical model of point rainfall DDF for the UK, especially relevant to longer return periods for reservoir safety evaluation. In addition, further analysis was carried out on ratios of winter/annual and summer/AMAX rainfall for each duration and return period, and concluded that simple predictive models for the ratios could be obtained using SAAR as a single explanatory variable. A new set of seasonal correction factors was derived to use alongside the all-year model. An alternative approach for setting initial conditions was developed based on revised models for setting C ini using the 1:2 year QMED and by reference to QMED estimates for observed data. For Scottish catchments, datasets suggested that there was no significant relationship between C ini and the magnitude of the event and no strong seasonal dependency (Wallingford Hydrosolutions ). However, this conclusion may be questioned on the basis of the events used for simulation, as addressed in the discussion.

METHOD
The analysis comprises the following: 1. The percentages of annual maxima of daily rainfall and flood peak flow, which occur in summer and winter, are mapped to demonstrate regional variations.
2. The concurrence of dates of AMAX daily and 6-hour rainfall and flood peaks is mapped and analysed.   The contrast between AMAX rainfall and flow frequency in summer for given ranges of SAAR is highlighted in Figure 2. At SAAR <700 mm, AMAX rainfall is above 70% and summer AMAX flows around 20%; the difference in frequency is more than 50%. Summer AMAX rainfall frequency falls steadily with increasing SAAR; falling below 50% at 1,000 mm SAAR, whereas summer flood frequency increases slightly at SAAR >1,000 mm, then remains steady for catchments with the highest SAAR levels. At SAAR >900 mm, there is a rapid fall in the difference so that at SAAR >1,000 mm, the difference is generally <20%, with a slow decrease at the highest SAAR. This analysis is based on daily rainfall AMAX but, as shown later, the discrepancy becomes even greater for AMAX rainfall of <1-day duration, typical of the design duration for catchments using RR methods.

Matching of daily AMAX rainfall and flow
The seasonal incidence of AMAX floods and rainfall is described above, but the following section looks in more detail at the concurrence of individual AMAX rainfall and AMAX flow events. Given the use of AMAX rainfall in the RR method of flood estimation, consideration is given to the frequency with which peak flow events are matched to annual rainfall maxima. In the first instance, matching is with respect to readily available daily rainfall AMAX (Figure 3(a)). Matching assesses whether or not a rainfall event could reasonably be considered to have generated a  The median design duration is 6.6 hours. The frequency of matching of 6-hour maximum annual rainfall with peak flow events was selected and is shown in Figure 3(b) and contrasted with that of AMAX daily rainfall.
Although the 6-hour dataset covers a shorter period than for daily rainfall, a regional comparison of daily and 6-hourly rainfall matching with flood runoff in Figure 3 shows clearly the reduction in matching for the shorter rainfall duration. Catchments with <10% matching dates are spread widely over southern and eastern England but even   is strikingly different from other catchments at 39%, higher than that for daily rainfall AMAX. This possibly reflects the rapid response to intense summer rainfall.

Matching of AMAX daily rainfall and AMAX flow in the given season
We now consider the percentage of summer and winter AMAX floods that are caused by AMAX daily rainfall in Although the percentage of AMAX flows that occur in summer is low (Figure 1(b)), the percentage of these events that are generated by an AMAX rainfall (biased towards summer) is high (Figure 5(a)). This is the case irrespective of location or catchment wetness; catchments with over 80% matching AMAX rainfall and summer flow occur from northwest Scotland to southeast England. This pattern results from either exceptional intensity or amount of summer rainfall or from an unusual coincidence (in dry catchments) between exceptionally high summer initial wetness and storm rainfall. In contrast, very few AMAX winter flows are generated from an AMAX rainfall event ( Figure 5(b)). This is especially the case in lowland

Seasonality of soil moisture content
River flooding depends not only on incident rainfall on a catchment but also by 'losses' mainly caused by storage and delay in soil and substrate. Losses vary not only by catchment depending on soil permeability but also by current soil moisture storage which depends heavily on rainfall seasonality and specifically on antecedent rainfall in the current season which determines soil moisture storage at the onset of a storm. The seasonality of soil moisture storage is investigated using soil moisture outputs from the Centre for Ecology and Hydrology Grid-to-grid hydrological model (Bell et al. ) with the 1-km grid aggregated to catchment averages. Four catchments with a range of wetness ( Figure 6) are used to compare between catchments and between months and seasons. For each catchment, the variability of monthly moisture storage is shown for 10%, 25%, 50%, 75% and 90% probability of occurrence in relation to the mean annual maximum soil moisture storage for the given catchment. We have focused on three catchments in the SAAR range where the contrast between seasonal rainfall and flow frequency AMAX is greatest and most rapidly changing with SAAR ( Figure 2). These also represent lowland catchments where economic activity and potential economic loss from flooding is greatest. Clog y Fan is used as a contrast. The analysis does not define field capacitysoil may be saturated and exceed field capacity. The catchments are as follows: • The Blackwater at Appleford Bridge is a dry lowland catchment in East Anglia with SAAR of 572 mm and an area of 247 km 2 with the bedrock of London clay and chalk overlain by boulder clay. Seasonally, 80% of AMAX flows occur in winter but only 26% of daily AMAX rainfall.
Just 20% of AMAX flows and daily rainfall AMAX are matched (and 7% of 6-hour AMAX rainfall).
• Instead, winter and summer rainfall statistics have been achieved by the manipulation of the annual data.
In our analysis, we have accepted the convention of considering seasonality in terms of two seasons: summer, where soil moisture deficits are usually high, and winter, where soils are expected to be close to field capacity. However, the potential flood risk varies continuously throughout the year.
If a RR method is to continue in use, perhaps it is time to reconsider the need for separate seasonal DDFs and the best subdivision of the year between winter and summer.
The perceived advantage of the RR method over the statistical method is in the provision of a design flood hydrograph, although the statistical method is widely recognised to give more reliable estimates of the probability of peak discharge estimates. An alternative method of synthesising a design hydrograph based on the generalisation of the shape of observed flood hydrographs was described by Archer et al. () and can be used in conjunction with estimates from the statistical method. This method has now been generalised for use in ungauged as well as gauged catchments and is widely used in Ireland (O'Connor et al.

).
However, given the limitations in addressing seasonality as well as the use of a single idealised unit hydrograph, con-

CONCLUSIONS
1. With respect to flood risk assessment, AMAX peak river discharge is always caused by heavy or intense rainfall (or snowmelt).
2. AMAX rainfall at 6 hours and daily only rarely causes AMAX flood (especially in dry catchments).
3. Thus, heavy rainfall is a necessary but not sufficient condition for flooding to occur.
4. AMAX daily and sub-daily rainfall occurs predominantly in summer; AMAX flooding occurs predominantly in winter.
5. The discontinuity between rainfall and flooding is explained by the consideration of coincident soil moisture storage.
6. On dry catchments, the seasonality of flooding coincides with the seasonality of soil moisture storage more than with intense rainfall.