A 249-Year Record of Floods at Appleby in Westmorland, UK

An analysis of nearly 250 years of flood records on the river Eden at Ap-pleby-in-Westmorland has enabled a flood frequency relationship to be established. The most severe floods were in the late 18 th and early 19 th century. With such a long history of flooding, some remedial measures would have been expected but the local people have, to some extent, adapted to the flood hazard by means of temporary and permanent flood proofing methods such as a cemented board across a doorway and removable flood boards. These measures were overwhelmed during the 2015 flood, as were the flood gates installed by the Environment Agency in 1998. A higher level of protection from floods at Appleby is called for.


The River, Rainfall, and Floods
The river Eden rises on the steep edge of the Pennine Hills and flows NNW towards Appleby, where it drains a catchment area of 337 km 2 (Figure 1). Below the town, the catchment lies in the rain shadow of the Lake District, an area of very high mountain peaks many in excess of 600 masl. The annual rainfall varies from over 2500 mm in the headwaters to about 900 mm at Appleby (UKMO, 1977) for the period 1941-1970, whilst for the period 1981-2010, it remains unchanged http://i.imgur.com/r/unitedkingdom/Lps9s0h. Land use is mainly peaty moorland on the high slopes with rough grazing and improved grassland on the lower slopes. With a catchment area of 337 km 2 , the river is most responsive to long duration rainfall from Atlantic depressions as in 1968 and 2015 (Smith & Tobin, 1979;Cumbria County Council, 2016). Floods have also been caused by summer convective storms such as in 1855and 1928, (Carlisle Journal 8/7/1855Cumberland and Westmorland Herald, 24/8/1828). Most floods are winter events, mainly due to the catchment size and response time of about 7 hours, as shown by gauging station records at Great Musgrave (Cumbria County Council, 2016).

Previous Flood Chronologies
Early studies by Graham Tobin as part of his Ph.D. thesis at Strathclyde University (Glasgow) (Smith & Tobin, 1979) identified 37 floods since 1815, grouping them into three classes according to their estimated size based largely on newspaper reports. Floods during the 18 th century were not considered. The British Hydrological Society website of historical events (www.dundee.ac.uk/geography/cbhe) reproduces most of this data, but misquotes Mannex (1851) in stating that the water level in 1822 was three feet (0.9 m) in Appleby church: the correct quotation is "In the great flood of 1822, the water was a yard deep both in the church and Rectory House" (Great Musgrave), which is 14 km upstream of Appleby. More recently, Watkins & Whyte (2008) gave a list of 34 severe events from a total of about 600 since 1686, covering the whole of the county of Cumbria. Since 2014, Darren Rogers (www.mauldsmeaburnweather.co.uk/floods.htm) has given a list of historic floods, newspaper reports of the serious events and photographs of the recent floods. However, he also identified additional floods not mentioned in Smith & Tobin (1979) taking place in 1816, 1829, and 1855. The severe flood of 1771 was described by Garret (1818) which marks the start of the present analysis. From the detailed descriptions of the events, the highest floods in chronological order are given in Table 1.

Interpretation of Flood Levels
The  "In houses, it removed dressers, tables & c… the water ran with a strong current along Bridge-street, and on the high side of the low cross; it also came down the church yard, and ran out at the church gates, tore up flags in the cloisters, and the pavement in the street" (Garret, 1818).
29/12/1816 "The Eden, at Appleby, Saturday night last was swollen to a greater extent than has been known for the past fifty years… and though the water ran higher than the arches it remains unshaken" (Carlisle Patriot 4/1/1816). "it ran like a torrent through the streets carrying away with it six carts" (Evening Mail, 8/1/1816).

1/2/1822
"… the water was six feet in depth in the stables of the King's Head inn. Such was the force of the torrent that the spray rose above the houses like a cloud. Many houses at the lower end of the town were immersed 5.5 feet in water" (Cumberland Pacquet 11/2/1822). "The water was two feet deep in Appleby church" (Westmorland Gazette, 9/2/1822).

21/8/1928
"In Chapel Street where the flood seemed to be worst, the tarmacadam was ripped off the road by the force of the running water, and houses were flooded to a depth of four and five feet. The road on The Sands was flooded to the extent of six feet" (Cumberland and Westmorland Herald, 24/8/1928). "At Appleby, the water rose to a height of six inches above the flood of New Years Day 1925" (Carlisle Journal 24/8/1928).

24/3/1968
"Appleby's only chip shop kept on frying until 9.30 pm when the water was lapping around the counter and they were forced to close shop… Even the Police Station which is about 4 ft 6 in above the road was flooded to a depth of 18 in forcing officers to move to an upstairs room. St Lawrence church was flooded to a depth of 2ft" (Cumberland and Westmorland Herald 30/3/1968). "About 250 properties, including 60 houses and many cars were damaged" (Cumberland News 29/3/1968). doors are present, may not be the same as that outside; for churches whose doors may or may not be closed this adds to the difficulty of interpretation.
The flood of 1822 is probably the highest since the level is stated as being six feet in the stables, which were located on the east side of the Eden. A field survey showed that the floor of these buildings is 127.7 m OD giving a flood level of 129.53 m OD. The flood of 1829 was described as being equal in height to that of 1822 and with no other evidence to suggest otherwise must be accepted. The flood of 1771 is clearly a very serious flood but for which no description of the level is given. However from the general damage and the flagstones in the Clois-  Table 2 shows that the rainfall intensity was higher in 1928 than in 2015.
The 36 hr depth at South Road, Kirkby Stephen in 1928 was 13 mm higher than 2015 as shown by the isohyet maps, Figure 3 and    During the early summer rainfall in the upper Eden was much greater than PE with 147 mm at Appleby; 157 mm at Kirkby Stephen, and 146 mm at Stainmore (old gauge). Daily rainfall for July and August until the 20 th was then combined with estimates of daily PE to give an estimate of the SMD for 19 th August. A summary of the results is shown in Table 3   Sands. In the Flood Investigation Report (Cumbria County Council, 2016) the reported flood level is the soffit of St Lawrence Bridge. This stands at 128.68 m OD but the surveyed level from the wrack mark on the church door is 129.04 m. The difference may be that the peak flow took place at night and could have been missed. Furthermore, the 1968 flood is reported by Smith & Tobin (1979) as also reaching the bridge soffit at 128.68 m OD. But residents stated that the 2015 flood was higher than in 1968. A check on this level was based on the newspaper description with 1.83 m floodwater along The Sands near the Police station. The result was 128.83 m OD, which needs to be reduced by the water surface slope because this location is above the bridge, to give 128.8 m OD making the 1968 flood lower than in 2015, in agreement with the statements of residents.
Less severe floods are difficult to distinguish and are therefore not included for analysis. Eye witness reports speak of the river coming to the top of the bank nearly every year, which is an occurrence that would not be reported as a flood. If levels reach nearby properties then an occurrence of about 1 in 3 years would be expected and this compares with 3.5 years (Smith & Tobin, 1979) and 3 years from the work of Darren Rogers (2019) (www.mauldsmeaburnweather.co.uk/floods.htm). In comparison, a value of 5 -10 years is given by Rogers from a report by the Environment Agency, but the lower limit of 5 years is too high since there have been over 70 reported floods in 200 years. The uncertainty is reduced by the evidence in Figure 5 which is a postcard, posted in 1907 and almost certain to be the flood of 26 th January 1903. The tops of the equi-spaced bollards are visible on the left hand side. These are still present and are 0.5m high. Calculation of the discharge at this level gives a value of 337 m 3 •s −1 which when compared with the flood frequency analysis below, has a return period of about 3 years. From these analyses and comparisons, it is now possible to calculate the flood discharge of the most serious floods.

Calculation of Flood Discharges
The ranked flood levels allow an estimate to be made of their respective dis-  one of which is shown in Figure 6. A postcard, which was sent from Appleby in 1903 ( Figure 7) looking upstream, shows that the river channel has remained sensibly unchanged for over 120 years. River discharge is calculated using the velocity area method, via the Manning equation: Q = V × A where V = velocity, A = cross section area. Q = discharge, V = R 0.666 S 0.5 n −1 . where R = hydraulic radius, S = water surface slope, n = Mannings roughness value obtained from (Chow, 1959).
The water surface slope was measured in the field and compared with the The n value was taken as 0.043 which is for a channel "clean, straight, full stage, no deep pools, but with stones and weeds and moderate meandering".
More objectively using equation 5.12 (Chow, 1959)    Discharge for the remaining floods was calculated and the results are shown in Table 4.  Allard et al. (1960), which give the user more confidence in the results.

Flood Frequency Analysis
Very few historical hydrology studies make estimates of very rare 10 3 -10 6 year events. The present author's work is an exception (Clark, 2014(Clark, , 2018 and as a  Note: Return periods calculated on the basis of record length (249 years) plus 20 years to make some allowance for the period of record starting with a flood (Reed & Bayliss, 2001). Return periods calculated using Clark (1983) Table 4 shows the estimates of peak discharge for the top seven events. Although the actual values of the peak discharge may be in error, and there is no way to get an exact answer, the frequency of flooding remains robust. the best estimates of the events will always plot as a straight line. Figure 8 shows the estimate of bankfull discharge with a rarity of around 1.1 years, within the range of 1.1 -4 years (Leopold et al., 1964;Williams, 1978;Edwards et al., 2019) most common for alluvial and gravel bed rivers. Also shown on Figure 8 is the threshold of flooding, the seven highest floods, and an estimate of the PMF based on the envelope curve of Allard et al. (1960), enhanced by Acreman (1989) and called the Extreme Catastrophic Flood (ECF). According to Allard et al. (1960), it will commonly occur on steep, wet, upland catchments such as the Eden at Appleby.

Estimating the Return Period of the December 2015 Flood Using Hydrometeorology
As an example of cross validating estimates of flood rarity, the author has developed a method based on rainfall frequency and soil moisture deficit (SMD) (Clark, 2007(Clark, , 2018. In essence, the rarity of a flood is equal to the joint probability of the flood producing rainfall and the threshold SMD. In terms of return period (1/p) the equation becomes: where: Rp ER = return period of the effective rainfall = (R − SMD).
Rp SMD Threshold = return period of the SMD at which runoff takes place. Rainfall frequency follows the methodology in Clark (2018Clark ( , 2019. During the winter period when the SMD (soil moisture deficit) is nil the equation reduces to: Rp flood = Rp ER or simply storm rainfall. Figure 3 and Figure 4 show areal distribution of rainfall for the 4 th and 5 th December. The storm started at 20.33hrs UTC on 4 th December. Peak discharge at Appleby was at 20.30 UTC on 5 th December and allowing one hour for rainfall to enter the main river gives an effective storm duration of 23 hours. The nearest TBR is at Scalebeck 7 km SSW of Appleby. Rainfall in this time period was 140.4 mm with a total of 189 mm for the two rainfall days. From Figure 3 and Figure  4, the catchment average rainfall for the two days was the sum of 39.9 mm and 64.7 mm. Scaling this rainfall in the effective rainfall time of 23 hours gives: (140.4/189) × (39.9 + 64.7) or 78 mm in 23 hours. Box 1 shows the detailed calculations of areal rainfall frequency.
BOX 1 Rainfall frequency estimation.
1 hr PMP = 160 mm (Clark, 2009, estimated from storm maximisation). For durations 1 -24 hr can be calculated using the logarithm of the duration and rainfall depth R = 228.225logD + 160 where D = duration (hours).
An estimate of the 2-year rainfall is obtained from the FEH (IOH, 1999). 23 hour 2-year areal rainfall = 44.1 mm (FEH CDROM). This estimate includes an areal reduction factor which is the ratio of point to areal rainfall for a given storm duration and area.
The logarithm of the two depths of rainfall, 37 mm and 235.3 mm are regressed with their respective y values of 0.1891 and 9.3826: Thus the rainfall frequency equation: logR = 0.0873y + 1.5516.
Thus for 78 mm in 23 hours y = 3.9002. The value of 3.9002 is used with Equation (2) to yield its value of T or return period. Return period = 53 years. End of Box 1. This compares with a return period of 47 years from the historic flood frequency analysis. The uncertainty of this estimate depends on the measurement of rainfall. Although the rainfall intensity was low there can be an underestimate of 5% which would give a return period of 59 years. On the other hand, the value of PMP may be an underestimate in the higher parts of the catchment and this would lead to a reduction in the return period. Overall, the event of December 2015 has an estimated return period of about 50 years.
The uncertainty in the flood frequency analysis has been reduced by the close agreement of the bankfull discharge calculated from channel dimensions and assigned a rarity of 1.1 years, the seven historic floods, the threshold of flooding from photographic evidence and discharge calculation of the 1903 flood event, and an estimate of the PMF which is consistent with the nationwide survey of historic floods (Allard et al., 1960) and brought up to date by Acreman (1989). Where these 10 estimates are correlated with their estimated frequency the result is r = 0.99 sig. 0.01%. By itself this does not constitute proof of accuracy, but shows that when flood estimates produced in different ways are related to their frequency there is a high degree of consistency. The hydrometeorological estimate of the rarity of the flood producing conditions would need a 9% reduction in the peak discharge of the 2015 flood to produce an exact match with the flood frequency equation. If this were correct then the threshold of flooding declines to a frequency of 1 in 4 years. The low level of uncertainty is shown by the estimates of bankfull discharge, threshold of flooding and the PMF being shown as open circles on Figure 8.

Human Response to the Flood Hazard at Appleby
It was Burton et al. (1968) who showed that control works are usually implemented when floods take place once every three years, so with such a long flood history it is instructive to see how people have coped over the past 250 years. Because

Discussion
Historically villages and small towns have had little or no consistent flood information available. It has been the existence of several good local newspapers in a fairly remote part of England that has been the main source of information.
The results show that notable floods occur about once every three years. Elsewhere this regularity of flooding has been enough to prompt significant remedial works where the frequency of positive certainty and adopted remedial works is about 1 in 2.5 years. Yet in spite of the Water Act of 1973 and subsequent legislation a good level of protection has not been provided for the town of Appleby. The reasons for this are more complicated than appears at first sight. One reason is that the townsfolk have largely adapted to the hazard by means of flood proofing and a warning system. Another may be a resignation to the problem which, apart from events like 1968, 2005, and 2015, do not cause huge damage Figure 9. Moveable flood barrier close to the west bank of the Eden at Appleby.

C. Clark
and are not perceived as life threatening: for example the 2004 flood at Boscastle in Cornwall brought swift engineering works at considerable cost, whereas Appleby has experienced many more flood events. It may be that an estimated rarity of 1 in 50 now assigned to the 2015 flood could lead to an economic justification for a better level of protection. It remains to be seen whether or not the effects of the rather inadequate self operated schemes have to be taken into account when a cost benefit analysis is carried out. But with an aging population, a flood stress-free lifestyle would be very welcome. A realistic identification of the flood frequency at Appleby is the first step towards this goal.

Conclusion
Taking into account a change in bridge cross section, an analysis of 249 years of recorded flood events, together with the use of hydraulic calculations to estimate the peak discharges, has allowed an estimate of the flood frequency for the river Eden at Appleby. To some extent, the result is validated by estimates of the bankfull discharge and the PMF. Land use changes in at least the upper part of the catchment have been minimal which largely avoids problems of non-stationarity in the record. However, changes may take place in the future of land use and climate. Further cross validation of flood rarity was achieved using the joint probability method. Another check related to the threshold of flooding of properties which is about 1 in 3 years. This agrees well with the detailed records of the more common flood events. Significantly the highest five events all took place before 1930, suggesting, that all else equal, very serious floods are now overdue, and that any interpretation of these future events must be tempered by what the historic record shows. Recent attempts by the Environment Agency to alleviate flooding at Appleby by means of flood gates have a low standard of protection. With over 100 domestic and commercial properties at risk, and with a resident population of just over 3000, many of whom live in the flood prone area, serious consideration should be given to producing a flood alleviation scheme with a high standard of design.