How extreme can unit discharge become in steep Norwegian catchments?

This study presents results of observations and analysis of the flood event in Utvik on 24 July 2017. Observations during and after the event, hydraulic simulations and hydrological modelling along with meteorological observations, are used to estimate the peak discharge of the flood. Although both observations and hydraulic simulations of flood extremes are uncertain, even the most conservative assumptions lead to discharge estimates higher than 160 m/s at culmination of the flood from the 25 km-large catchment. The most extreme assumptions indicate it may have been up to 400 m/s, but there is also strong evidence for the discharge at culmination being between 200 and 250 m/s. Observations disclosed that the majority of water came from about 50% of the catchment area giving unit discharges up to 18 to 22 m/s,km. If the entire catchment contributed it would be from 9 to 11 m/s,km. This is significantly higher than previously documented unit discharges in Norway and in the range of the highest observed peak unit discharges in southern Europe. The precipitation causing this event is estimated to be three to five times higher than a 200-year precipitation taken from the intensity–duration–frequency curves for the studied region. This is an Open Access article distributed under the terms of the Creative Commons Attribution Licence (CC BY 4.0), which permits copying, adaptation and redistribution, provided the original work is properly cited (http://creativecommons.org/licenses/by/4.0/). doi: 10.2166/nh.2020.055 om http://iwaponline.com/hr/article-pdf/51/2/290/682277/nh0510290.pdf er 2021 Oddbjørn Bruland Norwegian University of Science and Technology, 7491 Trondheim, Norway E-mail: oddbjorn.bruland@ntnu.no


INTRODUCTION
On 24 July 2017, the river Storelva in Utvik, Norway, grew from less than 1 m 3 /s to extreme ranges, which led to severe detrimental consequences within a 4-hour time frame. The event was documented through onsite observations of the course of the flood by the author. The purpose of this paper, besides documenting the event, is to assess how extreme this flood was in a Norwegian and European context.
Flash floods are floods caused by heavy and excessive rainfall of duration generally less than 6 hours or sudden release of water from, for example, dam breaks or ice jams (NOAA ). They are of the most dangerous and common natural hazards (Barredo ) and, as such, the threats that have the highest impact and likelihood of occurrence (World Economic Forum ). In the period 1950-2005, 2,764 casualties were documented in southern and continental Europe due to flash floods, representing about 40% of all flood-related casualties in Europe (Barredo ). In Norway alone, the yearly costs due to floods are close to 1 billion Norwegian krones (NOK) or about 100 million € (Finans Norge ). This does not include the rehabilitation cost of damage in water courses and on public infrastructure. Over the last 50 years, there has been an increase in the frequency and intensity of short duration rainfall (Sorteberg et al. ) and climate change will further enhance this. It is expected that precipitation-dominated catchments will experience an increase of flood frequency of up to 60% and that the challenges will be particularly pronounced in small, steep rivers and streams, as well as in urban areas (Hanssen-Bauer et al. ). This will have a significant influence on the design of infrastructure and the risk level and the risk assessments all Norwegian municipalities are required to carry out. Observations of floods in small, steep rivers are very sparse and extreme local precipitation is rarely captured by a coarse network of rain gauges, thus the basis for analyses and estimates necessary to estimate the risk from floods in such areas are very limited. As combinations of high water velocities and water levels can increase the risk acceptance level from a 200-to a 1,000-year return period (Ministry of the Environment ), the risk related to steep rivers is particularly relevant to study. In this context, extreme events like the Utvik flood can provide useful insights into how extreme such natural hazards can also be at these latitudes.
Can the observations carried out during and after the flood in Utvik be used to estimate the discharge and can this, based on a precipitation-runoff model, be used to estimate the intensity of the precipitation and finally reveal how extreme this event was in a Norwegian and international context? In this paper, several of the methods described by Borga et al. (), adapted to the available observations, are used to document and assess the magnitude of the Utvik flood.
The aims of this paper are: to use the in-situ and postobservations of the flood and flow over a dam crest together with hydraulic 2D simulations to estimate the discharge at culmination; to use rain gauge and radar observations together with hydrological modelling, observed lightning and eyewitness reports to assess how this event occurred, how extreme it was and to recreate the flood hydrograph and estimate the rainfall intensities causing the event; finally, to compare the peak unit discharge estimate for this flood to unit discharges of observed and reported floods in Norway over the last decade and to floods reported in southern Europe since 1950.

Norwegian floods
Based on historical sources, Lars Roald () provides an overview over major floods back to the 14th century. He mainly describes impacts and not discharges. Only at a few locations are flood discharges given. Thus, it is difficult to use these in a quantitative analysis without further knowledge and assumptions. Only since 2008, all floods observed at gauging stations in Norway and with a return period higher than ten years, have been systematically documented ( Figure 1). In November 2009, south-western Norway was exposed to high precipitation and several rivers flooded (Haddeland ). The highest observed precipitation was 143 mm over less than 12 hours. The highest unit discharge was 2.9 m 3 /s,km 2 . Locally reported damage indicate that in some areas the intensity probably was higher (Aftenposten ). In October 2010, a heavy rainfall event following several days of precipitation caused flooding in numerous rivers in the south of Norway, and the highest observed unit discharge was 3.04 m 3 /s,km 2 (Pettersson     (Equation (1)): where Q u is peak discharge in m 3 /s,km 2 and A is catchment area (km 2 ).

METHODS AND DATA
Hydraulic modelling and data for estimation of the peak flood discharge Storelva is an ungauged river and, even though traces of the maximum water level during the flood are visible at several locations, it is challenging to estimate the culmination discharge since the river is steep and the topography makes it

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O. Bruland | Extreme unit discharge in steep Norwegian catchments Hydrology Research | 51.2 | 2020 difficult to use hydrodynamic models. The best location to estimate the discharge is a dam crest ( Figure 5) at about 86 masl, where it can be estimated by Equation (2): where Q e is estimated discharge in m To validate the calculations, a 2D hydrodynamic model was established for the site in Hec-Ras v5.0 (Brunner b).
The terrain used in the model is based on high resolution lidar measurements from after the flood (Høydedata ).
The 2D simulation flow area (Figure 7) was selected to ensure stable inflow conditions. The gradient within the area is lower than 10%, the selected grid cell size was    Observations of erosion along streams in the catchment and along the main river coincide with the radar observations and indicate that the precipitation was not evenly distributed

RESULTS
Calculated discharge at the dam crest   at Utvikfjellet is up to two times higher than precipitation accumulated from the radar data, but the difference is less than the difference between precipitation observed by rain gauges and by the radar. The gauges showed 1.5 to 5 times higher 24-hour precipitation than estimates from the radar pixels (1 × 1 km 2 ) covering the gauge locations.
The runoff generation and accumulation from grid cell to grid cell and finally to the water courses within the region is also coherent with field observations and where  to 50% of the catchment, gives a unit discharge of this event from 9 m 3 /s,km 2 to over 17 m 3 /s,km 2 . In the most intense areas, the unit peak discharge can have been as high as 20 m 3 /s,km 2 .

DISCUSSION
There are several uncertainties related to the calculation of the unit peak discharge for the flood in Utvik in July 2017.
The dam crest is not ideal for the estimation as it is not perpendicular to the flow and, due to the high water level, the flow passes through sections without a defined crest. As the picture in Figure 6 shows, the flow was very turbulent, which makes it difficult to define maximum water levels and water velocities and as Figure 12 shows, the discharge estimates are dependent on the upstream water velocity.
In addition, unknown Manning numbers and a significant sediment load and bed load at peak discharge influences also the estimates of water velocities (USDA ). However, even though the river stretches far outside its original course and the bed load is significant, with a Manning of 10 which is low for a river with a clear defined channel, some pools and a rough bed (Chow ; Barnes ; Yochum et al. ), an upstream slope between 5 and 10% and a depth of more than 2 m, it is not likely that the water velocity was any lower than 5 m/s. Even if there are uncertainties regarding the flow through the side sections, the calculations show that more than 70% of the flow is where the crest is well defined and, and even with very conservative assumptions on the upstream water level and water velocities, the discharge would need to be higher than 200 m 3 /s.
The calculations using the dam crest formula (Equation (2)) give discharges that are coherent with the Hec-Ras simulations. According to Pappenberger et al. (), the uncertainties of hydrodynamic simulations are mainly related to the representation of the topography and the roughness, and according to Brunner (a), the 2D simulation in Hec-Ras is reliable at slopes lower than 10%. The slope is between 5 and 10% for the actual river section, the topography is detail mapped by lidar and the sensitivity to roughness is tested with Manning numbers from 7 to 20.
For inflows of 160 to 250 m 3 /s Hec-Ras gave water levels of ±15 cm compared to the observed depth at the same section of the river. As Figure 6 shows, there is significant damage higher up at the wall than the indicated maximum water level during the flood. Furthermore, the erosion extends higher up at the riverbanks than the simulated water levels. It is therefore likely that the water level at culmination used to determine the discharge is conservative.
Compared to pictures of reference rivers for roughnesses (Barnes ; Yochum et al. ), the roughness of the simulated river section is most likely in the range 10 to 20, which gives upstream velocities higher than 5 m/s. Hec-Ras gives velocities from 5.39 to 6.25 with these roughnesses. From Figure 12 this gives discharges from 223 to 267 m 3 /s. The sensitivity to water level and velocity reductions at the side sections indicate that these estimates can vary with up to ±9%. As the water level estimate used in the dam crest formula and comparison with Hec-Ras simulations is conservative, the upper range of the confidence interval, indicated in Figure 12, is more likely than the lower, at least for the lowest probable discharges. This was also the case for the event at Fulufjället in 1997 (Vedin et al. ). The weather as they described it, with very warm humid air prior to the event, was also comparable to the weather prior to the event in Utvik.
The radar observations support that the most intense area of precipitation covered a limited part of the catchment and that the total rainfall during the event was at least 70 mm in this region. Comparing the radar images with In the most intense area, it will have probably been higher. This is significantly higher than any documented peak unit discharges in Norway so far and even higher than the peak unit discharge reported for the 22 km 2 -large catchment at Fulufjället in 1997 (Lundquist ) that was estimated to be a 10,000-year event. Both these events are in the same range as peak unit discharges for extreme floods documented for southern Europe ( Figure 19).
Even when taking the identified uncertainties into con- and increased to 193 m 3 /s (7.95 m 3 /s,km 2 ) when including climate correction (Leine b). However, an estimate of the areal precipitation causing a flood of this size is, according to the IDF curves for the region, at least two to three times higher than a 200-year return period rain event Figure 19 | Unit peak discharges observed in Norway compared to the estimated most likely range of unit peak discharges for the Utvik flood, including the envelope curve suggested by Marchi et al. (2010).
(P 200 ) for similar duration. This indicates that the Utvik flood event was significantly higher than a 200-year event.
Prior to this event, Q 200 for a neighbouring, hydrologically similar, catchment was estimated to be 2.82 m 3 /s,km 2 , and 3.95 m 3 /s,km 2 including climate correction (Leine a).
Besides exposing the uncertainty of the Q 200 estimates, this indicates also that the suggested Q 200 for Storelva in Utvik is too high. Flood frequency analysis has significant impact on dimensioning and thus the cost of future infrastructure and also where people can live. Uncertainties like those identified in this case, illustrate the need of more information to base these analyses on to make them more reliable.

CONCLUSIONS
The Utvik flood is one of very few flash floods in Norway that are documented and quantified based on onsite observations during and after the flood combined with hydraulic and hydrological modelling. Analysis based on these observations and presented in this paper, shows that the discharge at the culmination of the Utvik flood most likely was in the range between 200 and 250 m 3 /s corresponding to a unit discharge of 9 m 3 /s,km 2 to 11 m 3 /s, km 2 . Assuming that the main contribution of the flood came from 50 to 100% of the catchment area, the peak unit discharge was from 9 m 3 /s,km 2 to 22 m 3 /s,km 2 . Hydrological analysis based on gauge and radar observations tuned to the estimated peak discharge and observed flood propagation, shows that the areal precipitation causing the event probably was higher than 114 mm over 3 hours and between 140 and 170 mm in the most intense areas of the catchment. It is also found that the peak unit discharges for the Utvik flood are significantly higher than for previous floods observed at gauging stations in Norway and comparable to the most intense flash floods observed in southern Europe.
Floods like this have a high societal impact and this paper documents how extreme they can also become at these latitudes. Their impact is not only through the damage they cause, but also indirectly as they influence design criteria for infrastructure. In respect to how important but uncertain estimates of design floods (Q 200 ) are in rivers like Storelva, as also documented herein, this paper tries to point out that there is clearly a need for more information about floods in small, steep and fast responding catchments in order to have a better basis for future decision-making in regard to infrastructure and societal and economical optimized mitigation measures.
This paper may also indicate that we are experiencing a new hydrological regime that makes previous observations less relevant and thus new ones are more urgently needed.