Heavy rainfall and flooding continue to cause problems in many parts of the world. Whilst flash floods are uncommon in small catchments it is even less common to have direct observations made during such events. When the observations include damage being caused to a dam then for several reasons it is essential that the engineering community be made aware. First, little is known about flash floods as they take place: most surveys and analyses are carried out afterwards, sometimes with a gap of many years. Second, the behavior of dam spillways under high or even moderately high discharges is not often observed and any information regarding weaknesses should be reported. Third, incidents at dams should be reported as standard practice (Charles, 2005). Fourth, reconstruction of an event may help to reduce the uncertainty amongst some of the hydrological and engineering community regarding the likely magnitude of the probable maximum flood (PMF), which can be used for design purposes (Midttomme & Tingvold, 2002; Koutsoyiannis, 2007; Lopez-Aviles, 2007; Clark, 2005a; Clark & Pike, 2007).

Any flood that has taken place which has not been recorded at a formal river gauging station, is a historic flood. This paper examines the evidence of a flash flood in a reservoired catchment located on the south side of the North York Moors UK, which took place on Sunday 19 June 2005 (Figure 1). The catchment area at the dam site is 2.99km^{2}. It is underlain by the Long Nab Member of the Ravenscar Group, better known as the Oolite group of limestone. However, the presence of some mudstone may account for there being both Stagnogley and Pelo-stagnogley soils covering most of the catchment. The topography is moderate to steep, with the land reaching 374m and falling to about 210 at the dam site. Land use consists mainly of coniferous forest with some grassland. The dam was built in the 1880’s and is located 1.5km upstream of the village of Boltby. It is an approximately 150m long and 20m high earthfill dam with a capacity of 121Ml (Claydon Pers. Com). The spillway consists of a weir on the east side of the dam which leads to a masonry spillway channel. Since it is situated upstream of Boltby it is designated a category A dam, such that the spillway must safely pass the PMF. A subsequent investigation of the incident gave a peak discharge of 32m^{3} s^{-1} and a return period in excess of 10000 years (Walker, 2008). No reasons for the flood estimate exceeding that provided by the ReFH (Kjeldsen et al 2005) at a return period of 150 years were given, neither was an estimated water balance described. In view of the importance of this event, especially with regard to the contemporary observations and photographs taken during the event, this paper seeks to reassess both the flood peak and more especially its rarity, thereby placing it in the wider context of risk assessment of UK reservoirs.

**Synoptic situation and antecedent catchment condition**

The UKMO holds digital data from synoptic stations that can be retrieved in order to produce weather maps. On the afternoon of 19 June a deep low lay over the northern Atlantic Ocean with associated warm sector of air lying over Britain. A surface cold front lying N-S was situated over western Scotland through Wales (Figure 2). During the afternoon this front moved eastwards. Another cold front lying aloft was situated some 190km to the east of the surface cold front. It was this second front which became associated with a line of storms that affected much of NE England, including the Boltby area.

The antecedent soil moisture deficit (SMD) was estimated using the relationships between monthly temperature and evaporation established at Charldon Hill Research Station (CHRS), but using local temperature data. This was then combined with daily rainfall data gathered at nearby Thirlby, 4.5km to the south of the catchment. The result for 19 June was 47mm.

**Estimates of storm rainfall**

There are three raingauges in the local area: Thirlby (NGR: SE 490841); Whorlton Moor (NGR: SE 480988) and Osmotherly Filters (NGR: SE 458968). The latter two gauges are only read every five or six days and therefore can give no information for the 19 June. The record at Thirlby was complete during June except for the day of the storm. The flood overwhelmed the gauge and the reading was lost. Reports of an empty beer glass being filled up by about 200mm of rainfall in about two hours have not been supported by the conditions of exposure where both in and out-splashing can occur. Walker (2008) also reports a reading taken at Hawnby, about 5km to the ENE, of 69mm in three hours. Also available as a source of rainfall depth is the UKMO Nimrod radar. This showed a band of very heavy rainfall >32mm hr-1 but lying to the north and NE of Boltby. Figure 3 shows the radar image for 14.30 GMT. The accumulated radar based rainfall for the storm over the Boltby catchment was 35mm. This must be regarded as a minimum because from 16.15-16.30 GMT the radar was not operational. In any case the estimate of 35mm is far too low to have produced the resulting flood. This result is to be regretted especially in view of recent reports on the quality of data (Harrison et al 1998, Smith et al 2006). Fortunately, a resident at Low Paradise, Chris Long, was present during the whole event. He reported that the storm lasted from 1500-1700 hrs GMT, and was so intense that visibility became very low and, having lived in parts of Africa, described the rain as tropical in character.

Although there are no reliable measurements of the storm rainfall, it is possible to estimate storm rainfall using the water balance equation from a knowledge of runoff volume, SMD, and percolation (Clark, 2005b).

**Rainfall = runoff + SMD + percolation**

However, in the case of the Boltby catchment the effect of the leaf litter under woodland has to be taken into account. This litter can be up to 20cm deep and its effect on water retention was measured in samples taken from the catchment and augmented by samples under the same land use in East Somerset. The average water retention based on six core samples of leaf litter was 39mm. An estimated hydrograph at Low Paradise is shown in Figure 4. Details of how the hydrograph was obtained are given in the next section. From Figure 4 the depth of runoff is 43mm. As noted above, the SMD was estimated as 47mm. An estimate of percolation was made based on a survey of 62 soil samples for their saturated hydraulic conductivity. The result, not shown here, gives a runoff rate of 78% for a rainfall intensity of 59.5mm hr-1 which is the sum of runoff, SMD and percolation, and litter storage corrected for % woodland. In order to get a runoff depth of 43mm, the effective rainfall (ER), assuming SMD = 0, when the catchment average leaf-litter storage of 29 mm has been fully taken up, can be estimated:

**Runoff depth = slope runoff + % runoff ( Rainfall – slope runoff)**

Where slope runoff (Clark, 2004) = Rainfall x Sine average

catchment slope (11.2º)

sine 11.2º = 0.194

Runoff = 0.194ER + 0.78 (ER – 0.194ER)

This gives an estimated effective rainfall depth of 52mm which potentially contributes to the runoff. About 0.194 of this rainfall becomes slope runoff and 22% of the remaining becomes percolation: 0.22 (52 – 0.194 x 52) = 9.2mm

Thus the water balance at Low Paradise becomes:

**Rainfall = runoff + SMD + leaf-litter storage + percolation**

**Rainfall = 43 + 47 + 29 + 9.2 = 128.2mm**

Since the storm took place in about two hours this result implies an average rainfall rate of 64mm hr-1 which is slightly higher than the value of about 60mm hr-1 which was used to estimate percolation. However, at this level of intensity a difference of 4mm hr-1 causes the % runoff to increase to 82% which results in an effective rainfall depth of 50.4mm and percolation of 7.3mm. The estimated storm rainfall thus becomes 126.3mm. This then gives a final value of 50.2mm for the effective rainfall.

**Resulting flood & estimates of peak discharge**

Soon after 1700 hrs GMT Chris Long walked from Low Paradise to Lunshaw Beck. By this time it was already in spate. Proceeding up to the dam by about 1830 hrs there was clearly damage being caused to the dam by the flood. Returning to Low Paradise he was able to take pictures of the flood which showed a rise in water level of about 1.5m, covering the shallower valley side slopes (Figure 5). Water was moving very fast near the watercourse and much slower over the whole width of the flooded valley. By about 2100 hrs GMT the beck had returned to its channel.

It has been possible to make three estimates of the peak discharge of the Beck, the location of which is shown on Figure 1. The reservoir was not being used for water supply and prior to the storm there was flow over the spillweir. Figure 6 shows details of two surveyed cross sections and the estimated water level. Three methods have been used to estimate the peak discharge: the method of Bagnold (1980) based on estimates of unit stream power and critical stream power at site 1, the weir equation at the da spillway – site 2, and the slope area method at site 3:

Slope area method: Q = A R^{0.666} S^{0.5} n^{-1}

Weir equation: Q = C BH^{1.5}

Unit stream power: ω = pQs/w

Critical stream power: ω_{c} = 290D^{1.5} Log (12Y/D)

Table 1 gives the definition of the variables in these equations.

The estimate of the discharge at site 1 – Windy Gill – using the method of Bagnold (1980), was made possible by the presence of cobbles which had been dumped some 80m above the reservoir. This method has been applied to the Cheviot Hills cloudburst of 1893, the 1770 flood at Lynmouth, and at Boscastle (Clark, 2005a, 2001, 2005b). A survey of the cobbles on site showed that the median diameter was 0.21m. By comparing the values of unit stream power and the critical stream power needed to move sediment of a given size under sensible channel roughness conditions, Figure 7 was prepared with roughness values of 0.06 and 0.07, which are representative of local site conditions (Chow, 1959). The result suggested a peak flow of 22-30m^{3}/sec.

Table 2 gives the results for all three sites wherein the result for site one was estimated based on a single value of the roughness and separate values for the channel and floodplain which took into account the shear between channel and floodplain flow (Lambert & Myers, 1998).

There is a reasonable consistency in the rates of runoff, with the highest rate coming from the smallest catchment area. The value of 10.1m^{3} s^{-1} km^{-2} from Low Paradise is higher than that from the spillway which suggests that the photograph taken of the highest observed level may not have been the highest reached during the flood. Alternatively the estimate at Low Paradise could have been too high by about 3-4m^{3}/sec. From the description of events at Low Paradise the water level shown in Figure 5 was the maximum. Furthermore, the presence of more pastureland below the dam would lead to a higher rate of runoff.

**Damage to Boltby dam**

Boltby dam was built in late Victorian times. The spillway was constructed of blockwork, each block weighing about 10kg. These were cemented together as a triple course. By the time Chris Long arrived at the dam this blockwork had already sustained considerable damage (Figure 8). Towards the distal end of the spillway the flanks of the dam also collapsed, suggesting some hydraulic undermining assisted by poorly compacted earth fill. No samples of this fill have been analysed for its mechanical composition or shear strength. Near the spillway the blockwork had also been ripped out by the force of water. Had the outflow discharge been much higher the damage to the spillway and dam would have been considerable. There was some slight but significant surface erosion on the flanks of the dam.

**Estimating flood rarity**

There are three main ways of estimating flood rarity. The first is to comparepeak discharge with a measured flood frequency curve – only suitable at a gauging station. Second, to calculate the flood frequency curve and then compare the peak discharge of the flood as in the first method. Third, to make use of the relationship between the return period of the flood, effective rainfall, and SMD rarity (Clark, 2007):

**Rp flood = Rp ER . Rp SMD**

Where Rp ER = return period of effective rainfall (rainfall – SMD); Rp SMD = return period of SMD. In the case of the Boltby catchment the effective rainfall also takes into account the storage by the leaf litter.

For very rare events such as the Boltby storm, the first two methods are unlikely to be suitable and in any case there are no gauged records on the Lunshaw Beck. There are also problems with extrapolation of the measured record, and on getting an estimate of the probable maximum flood (PMF) and relating it to floods of a lower magnitude. Where there is a well documented historic flood record then much greater confidence can be placed in the estimate of the rarity of a flood. In the case of Boltby, there is no historic record. Therefore the third method gives the best hope of obtaining a realistic result, always providing that the result passes suitable checks. These include comparing the rate of runoff from the PMF with results nationwide, simulating both the storm event and the PMF with a runoff model, and further checking that other methods such as the FEH cannot produce a similar result.

Using the method of Clark (2007) involves estimating firstly the return period of the antecedent SMD and secondly the return period of the effective rainfall. The median SMD for the end of June in Area 7 (Smith & Trafford, 1976), for an average annual rainfall = 808mm is 53mm. For an AAR = 900mm the median SMD = 46. Since the AAR for the Boltby catchment area is 839mm, the adjusted SMD becomes 53 – (7(31/92) ) = 50.6mm. This result then has to be adjusted for 19 June by linear interpolation between the date of the end of field capacity to 19 June: the result was 40.5mm. Two corrections are needed to this result. The first is for differences in evaporation between Smith & Trafford (1976) and the lysimetric record at CHRS, the second is for differences in rainfall.

For 19 June the ratio SMD (CHRS): SMD (Smith & Trafford, 1976) = 0.58. Therefore the median SMD corrected for differences in evaporation = 23.5mm. This has to be further corrected for differences in monthly rainfall between CHRS and the Boltby area (Table 3).

When these data are applied from the date of the end of field capacity to 19 June the median SMD increases to 25.5mm.

In order to determine the frequency of SMD at Boltby the equations for the end of May and end of June for CHRS (Clark, 2007) have to be interpolated and adjusted for the median SMD for Boltby. The full set of equations for the months April to September have been revised and are included here for reference (Table 4).

Interpolating the regression slope for 19 June gives SMD = 25.778y + intercept. Substituting a value of 25.5 for the median SMD and 0.189 for the value of y at the median return period of two years yields:

**SMD = 25.778y + 30.372** (1)

The SMD on June 19 was 47mm, therefore using equation 1 gives a return period of 1.32 years.

The estimated storm rainfall was 126.2 in two hours. The effective rainfall will be total rainfall – SMD and leaf litter storage = 50.2mm. Assuming that the rainfall was evenly distributed during the storm then the 50.2mm may have occurred in 0.8 hours. A 0.8 hour rainfall frequency curve was calculated using estimates of 24 hour PMP (Clark, 2002) and maximised storms with a duration of one and two hours. Log linear regression of the results gave:

**R = 182.246 Log D + 147.866**

Where D = duration (hours) R = rainfall (mm).

This equation allows an estimate of 0.8 hour PMP of 130mm. An estimate of 2-year 0.8 hour rainfall (Kjeldsen et al 2005) for the Boltby area = 11.5mm. Thus the all year rainfall frequency equation becomes:

**Log R = 0.11457y + 1.03904**

For winter the two year 0.8 hour rainfall = 6.5mm and the equation adjusted assuming an identical growth rate:

**Log R = 0.11457y + 0.79125**

Since the storm took place on 19 June the likely frequency relationship will exist somewhere between the all year and winter extremes. The seasonal adjustment factor (Clark, 2007):

**SF = 0.5 [ Sin ( D – 122 – 0.01369D) + 1 ] **

Where D = the day of the year with January 1 = 1.

In the present case SF = 0.857. This result is then applied to the intercepts of the all year and winter rainfall frequency equations:

**I _{SADJ} = SF [ I_{s} – I_{w} ] + I_{w}**

Where I_{SADJ} = seasonally adjusted intercept; I_{s} and I_{w} = intercepts of the all year and winter frequency relationships. In the present case I_{SADJ} = 1.0036 to give the seasonally adjusted frequency equation for Boltby:

**Log R = 0.11457y + 1.0036** (2)

This equation is based on point estimates of rainfall. The estimated effective rainfall depth of 50.2 is the areal average rainfall and must be adjusted using an area reduction factor (ARF) to obtain the value of point rainfall which can then be applied in equation 2. The area reduction factors of the FEH (IOH, 1999) do not take into account the changing spatial variation of storms with storm rarity. Rare storms tend to have steeper spatial rainfall gradients than more common ones. The problem of the ARF has already been the subject of debate (Bell, 1976; Kelway, 1975; IOH, 1977). Data in Bell (1976) suggest a decrease in ARF with increasing storm rarity. While the ARF’s in the FEH may be appropriate for storms whose return period is less than 30 years, the design engineer is often concerned with much rarer events.

At the same time as accepting the use of storm centered ARF for PMF calculations (IOH, 1999) it should not be automatically ruled out for rare events which are less than PMP. Therefore the ARF-rarity problem has been investigated by taking the most severe 1 hour, 14 hour, and 69 hour storms, namely those at Oxford in 1967 (McFarlane & Smith, 1968), Martinstown in 1955, (Clark, 2005c), and Castleton in 1930, (British Rainfall, 1930). The ARF for these storm events in relation to area was calculated from isohyet maps. In order to get the lowest area reduction factor (ARFmin) for these events the moisture maximising factor (MMF) was applied in the same way as for maximising the rainfall, but inversely, that is as the reciprocal of the MMF. The result is shown in Figure 9 where the ARF’s for other storm duration have been calculated using a log-linear relationship between storm duration and the ARF. The values of ARF for any return period are then estimated:

**ARF _{T+ 1.5} = y exp ys/9.382**

where ARF_{T+1.5} = Areal reduction factor for a given rarity, y = [ ( -ln ln (1 – 1/T ) – 3.3842 ) 1.09348 T –0.046518 ] + 3.3842 (modified reduced variate), s = Log ARF_{min} / Log 9.382. The 0.8 hr ARF_{min} is estimated from a log-linear of ARF_{min} and storm duration using 1 hr and 72 hr data: 0.8 hr ARF_{min} = 0.061916 Log D + 0.85, where D = storm duration. Therefore 0.8hr ARF_{min} = 0.84399. Thus s = -0.07576 and ARFT+1.5 = 0.915.

To apply the method to the Boltby areal effective rainfall of 50.2mm, the return period of the point rainfall at the same depth is calculated using Equation 2 to give 870 years. The ARFT+1.5 at Low Paradise = 0.915. This produces a point rainfall of 50.2/ 0.915 = 54.9mm. Therefore the return period of the point rainfall which gives an areal depth of 50.2mm = 1459 years. Then the return period of the flood event:

**Rpflood = Rp ER . RpSMD **

= 1459 . 1.32 = 1926 years

There will be some uncertainty in this result which can, to some extent, be tested by placing it in the context of floods which occur over the entire range up to the PMF which has a return period of 106 years. Calculation of bankfull discharge at Low Paradise gave a result of 1.6m^{3}/sec. There is no natural channel at the dam site so this result was reduced by the ratio of catchment areas. The result was 1.2m^{3}/sec. An estimation of the PMF was obtained using the non-linear flow model (Clark, 2004) using a time to peak relationship for the upper Brue and adjusted for mainstream channel length. Quickflow was estimated from a survey of soil saturated hydraulic conductivity in the catchment. Rainfall input was based on the PMP (Clark, 2002) and historic storms of shorter duration. Delayed flow was also calculated as per the upper Brue but with a delay of 0.5 hour in view of the smaller catchment. The result was 96m^{3}/sec. This result, together with that for the 2005 storm and bankfull discharge were displayed on extreme probability paper (Figure 10). Also shown are the results of applying the ReFH (Kjeldsen et al, 2005) at the dam site up to the 150 year event, estimates of PMF using the FEH (IOH, 1999), the ICE (1996) rapid method for PMF estimation, which gave the same result as the FEH, and the results of Walker, 2008). There is a good agreement of the PMF values from the FEH and ICE methods. However, the estimated discharge for the June 2005 storm was close to these estimates, even though the areal rainfall was only about 128mm. This is considerably less than FEH PMP, and even lower than the two hour PMP of Clark (1995, 1999) based on separate analyses. There is also a change in flood growth rate above the ReFH 150 year event towards the FEH PMF. Furthermore, a PMF of about 32m^{3}/sec gives a rate of runoff of only 10.7m^{3}/sec km^{-2} which is just above the normal maximum flood envelope (Allard, Glasspole, & Wolf, 1960). For a catchment area of 3km^{2} there have been several flood events whose rate of runoff is much higher. Since the Boltby catchment is roughly fan shaped with steep valley sides and relatively thin impermeable soils, then there are serious doubts about the FEH/ICE estimate of the PMF. The results of Walker (2008) are more realistic but only give a PMF of about half that reported in this paper. However, the estimated rainfall for the Boltby incident was given as in excess of 200mm. If this was correct then the flood volume at Low Paradise would have been about three times larger than that shown in Figure 4, a result which is untenable.

In respect of the present results, there is a very good linear correlation between the PMF, 2005 flood, and bankfull discharge. The PMF based on this flood frequency analysis is 111m^{3}/sec, close to the estimate of 96m^{3}/sec from the non-linear flow model. The lower result gives a rate of runoff similar to that during the Bowland forest flood of August 1967 (Hydraulics Research Station, 1968). The flood growth curve at Boltby is steeper than that of the rainfall: under grassland this would not occur. This effect of land use on flood growth rates was envisaged in 1987 by Clark (1987) since the magnitude of frequent floods is reduced by forest cover. This effect decreases with increasing flood rarity thereby giving a steeper flood growth curve.

In order to give greater confidence to either or none of the results the Boltby flood was simulated using the estimated SMD and rainfall using the non-linear flow model and FEH. Table 5 shows the results.

In applying the FEH to simulate a notable event, the SMD of 47mm was applied. It is important to note that the FEH favours MORECS as a source of SMD values which in this case was greater than 47mm which would have led to a lower peak discharge. The time to peak was taken from the actual event: 1.25 hours, which is much less than the standard time to peak of the FEH. The non-linear flow model used its own formulations. The peaky storm profile for the FEH included a period of 0.5 hours with 88mm, which is close to the 0.5 hour PMP. The results showed that the non-linear flow model gave a reasonable result with uniform rainfall whereas the FEH was about 10m^{3}/sec too low, an error which was hardly reduced by the use of a more peaky rainfall profile. This is because the FEH rainfall runoff method is not particularly sensitive to rainfall intensity when rainfall depth is held constant.

**Summary and discussion**

The Boltby storm had a rainfall depth of about 130mm in two hours. This has a return period of about 1000 years. The return period of the resulting flood is estimated at about 1900 years, which is considerably less than a previous estimate. The flood caused considerable damage to the spillway of Boltby dam and a part of the embankment. Estimates of the PMF at the site suggest that a flood four times this event can take place, which would have a rate of runoff comparable to other floods in the UK. Estimates of the flood frequency at the dam site were made using two different methods. The non-linear flow model gave sensible results when compared with data from the Boltby storm and an estimate of bankfull discharge, while the FEH gave results much too low, especially in view of the Boltby storm.

The expected rate of runoff from the extreme catastrophic flood (Allard, Glasspole, & Wolf, 1960), is much higher than the PMF at Boltby and indeed for other recorded floods in the UK. This suggests that for catchments smaller than about 10km2 the expected rate of runoff of their ‘extreme catastrophic flood’ may not be attained. Nevertheless, a PMF of about 100m^{3}/sec is more than 2.5 times that produced by the FEH, which if correct has serious implications for dam safety in the UK. There is a need for dam owners to reassess the spillway design flood of all category A dams. In the case of Boltby dam the Yorkshire Water Services seemed to be unaware of its existence when Chris Long phoned the authority, informing them of the damage being done at the time. It might have been a case of mistaken identity, but the signature of what could have happened at Boltby was very much in evidence on Sunday 19 June 2005.

*Colin Clark, Charldon Hill Research Station, Shute Lane, Bruton, Somerset, England BA10 0BJ. Email: colin4chrs@hotmail.com*

*The author would like to thank Chris Long for providing copies of his photographs and description of events on 19 June. Graham Bartlett (UKMO) kindly provided copies of the synoptic charts; the British Atmospheric Data Centre provided the radar image; Christine McCulloch gave useful comments on an earlier version of the paper*

Tables

Table 1

Table 2

Table 3

Table 4

Table 5