Quantitative interpretation of risk potential of beach erosion due to coastal zone development

Coastal erosion is more severe due to human-induced coastal zone development in addition to natural climate change. Anthropogenic development affecting coastal erosion is divided into three areas; watersheds, coastal waters, and coastal land areas. In this study, the ultimate effect of anthropogenic development on changes in the amount of sand, changes in the littoral 10 drift, and changes in shoreline variability in these three planar areas is expressed as quantitative risk potential of beach erosion damage, defined as a change in the planar surface of the sand beach. The change in the amount of sand is due to the law of conservation of matter, and the littoral drift characteristic of sand is interpreted as a change in the main crest line at the breaking point, and the response characteristics of shoreline position is interpreted as change in the erodibility and recovery characteristics of beach sand. This quantitative method was applied to Bongpo-Cheonjin Beach of erosion grade D (frequency 15 of erosion damage within 5 years) in Gangwon-do, Korea to identify the cause of erosion and evaluate the detailed applicability of this method. It was interpreted using a series of aerial photographs taken from 1972 to 2017 and survey data obtained from the erosion rating project started in 2010. In the erosion rating project, the GPS shoreline survey of 4 times per year and the sand sampling at the swash zones of base line at 150m intervals are mainly carried out. We showed the feasibility of methodology evaluating the risk potential for beach erosion proposed in this study, and it can be expected that this method will 20 be applicable to eroded beaches elsewhere.


Introduction
In recent years, erosion of sandy beaches has intensified in many countries due to the complex effects of climate change (i.e. global sea-level rise), reduced coastal sediment budgets (e.g. due to changes in watershed environment), and deterioration of 25 coastal environments (e.g. caused by artificial structures and human interference). More seriously, the scale of development to coastal environments has threatened beach safety through (1) changes in nearshore wave fields following the installation of harbor structures, (2) permit of inappropriate large-scale reclamation without preventive measures, (3) decrease in beach buffer width with the construction of roads and infrastructure, and (4) reduction in the upstream sediment supply.
https://doi.org/10.5194/nhess-2021-180 Preprint. Discussion started: 8 July 2021 c Author(s) 2021. CC BY 4.0 License. the section where the equilibrium shoreline retreats due to a change in the wave field, or a temporary retreat of the shoreline due to the influence of sand suspension and offshore transport under the storm wave incidence. Although the physical processes that cause erosion are characteristically subdivided as described above, independent research on each erosion process has been actively conducted, but it is rare to find out the cause of erosion by quantitatively evaluating all erosion processes. The 45 following is a summary of research contents on the budget analysis, longshore sediment transport, and cross-shore sediment transport process that contributed to the quantitative recognition of this study.
The beach maintains its current volume as the sediment budget is balanced. Therefore, it is essential to analyze it by dividing it into littoral cells, which are the zones that affect the sedimentation budget as done by Inman and Jenkins (1984) and Bray et al. (1995) and so on. When the amount of sediment discharge into or leaving in the littoral cell changes, a new equilibrium 50 volume of sand is established in the beach accordingly (Dolan et al., 1987;Kana and Stevens, 1992;Pethick, 1996;Cooper, 1997;Cooper and Pethick, 2005). Therefore, the amount of sediment entering into the beach from the river and the amount of sediment leaving into the open sea by the continuous wave action should be interpreted as the main impacts of the sediment budget. For example, a decrease in sediment discharge due to the construction of dams in rivers (Foley et al., 2017;Warrick et al., 2019) or an increase in sand loss due to sand mining (Edward et al., 2006) causes gradual shoreline retreat. And Lee and 55 Lee (2020) proposed an equation to calculate the beach width according to the law of mass conservation by placing variables representing two main factors about sediment budget.
It is assumed that the longshore sediment transport alters the feature of shoreline, but does not change the quantity of sand in the littoral cell. Thus, this results in deposition in some areas, but at the same time, erosion in some areas. Numerous observations and studies have been conducted to estimate the correlation of longshore sediment transport rate to wave and 60 sand environments (Komar and Inman, 1970;CERC, 1984;Kamphius, 2002;Bayram et al., 2007). However, it is still mostly dependent on the empirical models in estimating the equilibrium shoreline in the vicinity of harbor breakwaters or coastal structures. Among them, the parabolic bay shape equation (PBSE; Hsu and Evans, 1989) has been recognized for its utility in https://doi.org/10.5194/nhess-2021-180 Preprint. Discussion started: 8 July 2021 c Author(s) 2021. CC BY 4.0 License. many countries and is being used for coastal management (USACE, 2002;Herrington et al., 2007;Bowman et al., 2009;González et al., 2010;Silveira et al., 2010;Yu and Chen, 2011;Anh et al., 2015;Thomas et al., 2016;Ab Razak et al., 2018a65 & 2018b. Recently, Lim et al. (2021) applied the empirical equation of parabolic equilibrium shoreline of Hsu and Evans (1989) to the polar coordinate fitting the shoreline to prove its versatility for general sand beaches.
Lastly, cross-shore sediment transport causes morphological changes in the beach profile due to the wave, causing shoreline retreat. Much work has been done to interpret geomorphological phenomena (Swart, 1974;Wang et al., 1975;Wright et al., 1985;Miler and Dean, 2004;Yates et al., 2009;Montaño et al., 2020). Recently, Kim (2021) proposed a method of estimating 70 the erosion width by frequency through statistical analysis of GPS shoreline observation data observed by season for more than 10 years. Kim (2021) also devised the concept of horizontal movement of suspended sediments and applied a wave scenario model to analyze the response relationship between the convergent MSL of Yates et al (2009).
In this study, the ultimate planar area of beach erosion occurring in the beach according to the anthropogenic factors that induce beach erosion is obtained, and the process of estimating the consequence of beach erosion damage corresponding to the area 75 of the erosion zone that is damaged is introduced. In addition, a method of estimating the frequency according to the beach erosion width from the survey data of shoreline variability and, finally, a method of quantitatively estimating risk potential is presented. The risk potential is expressed in terms of the beach planar area, and it is ultimately equivalent to the area of erosion damage received from development activities, although it is unknown when the impact will be completed.
The encroachment accumulation curve, which calculates the area of the encroached section of the beach according to the 80 erosion width, corresponds to the vulnerability curve. Here, the erosion width corresponds to the hazard, and the erosion width from the average coastline due to anthropogenic development includes the development of watershed areas, coastal waters, and coastal land areas. The erosion width is accomplished through three different planar areas; (1) the planar area of the beach that is ultimately reduced due to the development of watershed areas, (2) the planar area that is ultimately eroded due to the change in the wave field due to the development of the coastal waters, and (3) the planar area that is temporarily eroded due 85 to the occurrence of cross-shore transport due to the periodic high wave incidence. Assuming that the total eroded planar area obtained in this way evenly affects the entire beach length except for a part of the deposition section due to shoreline deformation, it is divided by the beach length L to finally obtain the beach erosion width corresponding to the hazard strength.
The methodology presented in this study is applied to the Bongpo-Cheonjin Beach, South Korea, a coast with a high risk of erosion, and the validity of the methodology is verified. 90 After a brief introduction in section 1, section 2 of this paper discusses the erosion risk potential using the concept of the encroachment accumulation curve. Section 3 of this paper discusses methods for quantifying three erosion potential mechanisms: (1) sediment reduction from an updrift river, (2) longshore sediment deposition causing beach erosion following harbor breakwater construction in the downdrift region, and (3) shoreline retreat due to cross-shore sediment during high waves. concluding remarks are given in Sect. 6. It is expected that this quantitative method for identifying the risk to beach erosion could be applied to similar coastal environments on the eastern coast of the Korean Peninsula, as well as elsewhere in the developing and developed countries. 100

Beach Erosion Risk
Recently, in several countries including the United States and Europe, the analysis of coastal impact caused by extreme events such as hurricane is increasing (eg Beven II et al., 2008;Kunz et al., 2013;Van Verseveld et al., 2015;Spencer et al., 2015). Sanuy et al. (2018) established an erosion risk assessment method based on the Bayesian network, and searched for a method to reduce erosion by applying it to beaches located in the Mediterranean. In addition, many studies have been conducted to 105 evaluate coastal risks through analysis and prediction of various physical phenomena and effects using numerical models (eg Roelvink et al., 2009;McCall et al., 2010;Harley et al., 2011;Roelvink and Reniers, 2012).
However, most risk assessment methods are not only focused on extreme events, but also require numerous data and techniques, so it is not practical for coastal managers to apply them to real fields for coastal erosion management purposes. Therefore, in this study, we suggest a method to assess the ultimate risk (risk potential) of erosion damage using a set of minimal data such 110 as existing aerial photos or techniques estimating the sediment load reduction due to watershed development, shoreline survey data, sea area development and deployment plan, and encroachment status without additional field observation at the time when coastal development is planned.

Definition of beach erosion risk
Risk is defined as the time-averaged amount of damage, and the evaluation is possible through time domain, frequency domain, 115 and probability domain analysis. In general, in the expression of the frequency domain, risk is defined as the product of consequence and frequency as shown in the following equation,

=
(1) The risk potential (ultimate risk) in this study is the value corresponding to the consequence of the right side of Eq. (1), and is defined as the planar area ultimately damaged by erosion according to the development of watersheds, land, and coast. The 120 sand buffer zone does not cause damage even if erosion occurs, and is excluded in the damage evaluation as a section that recovers over time. And the frequency on the right side of Eq. (1) corresponds to the frequency of erosion from the equilibrium shoreline to the erosion width. This value represents the erosion vulnerability of the beach and is obtained under the assumption that there exists erodible sandy beach.

Risk potential of beach erosion 125
Quantitative estimation of Consequence is made from the analysis of all factors affecting the planar area change of the beach.
As already mentioned in the introduction, coastal erosion occurs due to imbalance in the sand budget, changes in wave fields, and shoreline retreat due to high wave incidence. As such, the physical process that causes erosion is characteristically subdivided, so the erosion consequence is calculated through the sum of the independently calculated erosion planar areas.
(1) The planar area that is reduced due to the lack of sand budget is called the sediment budget reduction potential , (2) the 130 planar area newly deposited as longshore sediment transport due to the change of the wave field is called the longshore sediment deposition potential , and (3) the planar area that is retreated from the shoreline due to the high wave incidence is called the cross-shore sediment retreat potential . The erosion width is measured shoreward with respect to the equilibrium shoreline. For the previous two cases, the concept of frequency is not established, but for the last, beach erosion due to high wave incidence, the frequency is estimated through the statistical analysis of shoreline survey data. 135 Since the sum of the planar areas of erosion includes a buffer zone in which no damage occurs, the value itself does not become a risk potential and is obtained through an encroachment accumulation curve according to the erosion width from the equilibrium shoreline. A sandy buffer zone indicates an area unaffected by storm/high waves for a specific number of years, thus where sediment is recovered as it is after storms. The following introduces the method of obtaining the erosion width from the equilibrium shoreline from the erosion planar area and the method of extracting the encroachment accumulation 140 curve.
It can be assumed that the total planar area of erosion affects the entire length of the beach, excluding a short part of the deposition section due to shoreline deformation, and thus dividing by the length of the beach , the shoreline retreat can be obtained as follows.
The right-hand side of Eq. (2) includes the effect of (1) reduction in sediment budget from river supply , (2) alongshore sediment deposit due to harbor breakwater construction , and (3) cross-shore sediment retreat by high waves which has different values depending on the frequency. When is calculated, as shown in Figure 1, the overall erosion consequence can be obtained from the encroachment accumulation curve that accumulates the area to be damaged by the hinterland development of the buffer section based on the average shoreline.  The following introduces the method of extracting an encroachment accumulation curve. It is a curve that accumulates the encroached area with respect to the shoreward distance from the average shoreline. If the circle that best fits the current average 155 shoreline is obtained, the center of the circle can be obtained. As shown in Fig. 2, the average shoreline is located at from the origin of the circle, and the encroached boundary (red dashed line in Fig. 2) is located at from the origin. Of course, each angle α has a different value depending on the encroached aspect. Therefore, if and are determined for each angle , the encroachment accumulation curve is obtained by the following equation according to the shoreward distance from the average shoreline. 160 where,

Calculation process of the beach erosion risk
In Eq. (2), is the shoreward coordinate from the average shoreline, and if shoreline retreat of Eq. (2) is substituted for , the erosion width invades the encroachment zone and the planar area where damage occurs is obtained. This area corresponds 170 to a consequence of Eq. (1), where frequency can be regarded as a one-year frequency in the case of and , on the other hands, depends on the frequency of high wave incidence. Therefore, if concepts of the erosion potential and the encroachment accumulation curve are applied, the risk in Eq.
(1) is expressed as the following equation.
where = ( + ) and = ( ) − . 175 In general, and mean the ultimate retreats of the future shoreline from the current shoreline position, respectively and are considered smaller than . Therefore, if the buffer section is sufficient, hardly occurs, so the first term on the right side of Eq. (5) is judged to be insignificant. The methodology of quantitatively estimating the variables appearing in Eq. (5) is described in Sect. 3.

Sediment budget reduction potential
The sediment budget reduction potential is defined as the reduction in the planar beach area mainly followed by the lack of river sediment load due to the watershed development. Applying the law of conservation of matter to the beach of the littoral cell (Lee and Lee, 2020), it can be expressed as where is the rate of sediment discharge into the beach and is the sediment discharge leaving from the beach.
Representing is the amount of sediment from the river and representing is the sediment discharge lost to the sea due to the action of waves. If we express the loss rate due to wave action as a function of the constant value of sand loss rate , the following equation is established: where beach volume can be expressed as the product of the vertical height of littoral zone and beach planar area , assuming that , the sum of berm height and closure depth, is constant along the beach. The sand loss rate can be calculated from the sediment amount entering the beach. Therefore, Eq. (7) becomes the following equation: A detailed description of the seaward loss of suspended sand due to wave action, , expressed in , is presented in Lee 195 and Lee (2020). If Eq. (8) is applied to the steady state and decreases by α due to watershed development, forestation, or river maintenance projects, it also decreases by α in beach area, as in the following equation; Here, the superscript 'o' corresponds to the beach area before development. This reduced beach area Δ is defined as the sediment budget reduction potential (Fig. 3). Assuming that is uniformly spread over the entire embayment with a 200 curved length of , then beach width reduction can be estimated by = . (10)

Longshore sediment deposition potential 205
The longshore sediment deposition potential is defined as the planar area of the depositional zone caused by the deformation of the shoreline due to wave field changes. The parabolic bay shape equation (PBSE; Hsu and Evans, 1989) is applied to delineate the shoreline feature in static equilibrium and simply recognize the ultimate bay shape formed after the construction of a harbor breakwater. This equation can be used to define two adjoining regions with a common tangent at the downdrift control point E (Fig. 4): 210 where 0 is the length of the control line (FE) joining the parabolic focus (F; wave diffraction point) and the downdrift control point (E), ( ) is the radius from the focus to a point Q on the equilibrium shoreline, is the perpendicular distance from the wave crest baseline to point E, is the angle between the wave crest baseline and the line joining the focus and the control 215 point, is the angle between the wave crest baseline and the line connecting F and Q, and 0 , 1 and 2 are the coefficients provided by Hsu and Evans (1989). The approximate expression of the PBSE can be given as, In Eq. (13) and Fig. 5, ′ is the angle between the headland (i.e., the breakwater tip) and coastal structure (e.g., harbor breakwater) or longshore sediment control facilities (e.g., groin). For application, Eq. (13) can be approximated as,

Cross-shore sediment retreat potential
The cross-shore sediment retreat potential is defined as a planar beach area that is temporarily eroded by high wave incidence. To estimate the maximum width of beach erosion within the specific period, a minimum number of seasonal measurement data are required. If the observed shoreline data follow a normal distribution, then the data can be applied to assess the 245 maximum probable erosion occurring once in years with a probability of 1 4 in a cumulative normal distribution curve. From the cummulative curve of normal distribution, the frequency (F) for a shoreline variable can be determined by, From Eq. (16), the erosion width ( ) is then calculated for a shoreline variation width ( ) by, where is the mean beach width and is the standard deviation of the shoreline variation width obtained from the data distribution curve. However, this value represents only the erosion width based on the data collected four times per annum.
Unlike measurements taken at regular intervals, different erosion widths may exist at any time when measurements were not taken; hence, the actual value could be larger than that measured and presented in this paper. The eroded beach width due to the cross-shore sediment retreat potential with a certain return period ( ) can be estimated statistically from shoreline 255 The mentioned in Eq. (16) corresponds to the cross-shore sediment retreat potential divided by the standard deviation of shoreline variation. The frequency ( ) corresponds to frequency in the erosion risk potential given in Eq. (5).
However, since the shoreline was observed four times a year, it was approximated by multiplying 1.5 to convert it into a daily 260 statistical value of the variation. Table 1 shows the shoreline data variation and the corresponding daily shoreline retreat per frequency . If the method suggested above is not applicable because the amount of shoreline data is not sufficient for statistical analysis, 265 then wave data and sediment grain size ( 50 ) should be used (see method in Kim and Lee, 2018), based on storm-wave-induced erosion on an equilibrium beach profile (Dean, 1977). This gives the total planar area of beach erosion, = where is the shoreline length of the affected beach area.

Study site description
The quantitative interpretation proposed in the present study is applied to the beach erosion problem at Bongpo-Cheonjin Beach (38°15'N, 128°33'E), located in the northeast of Gangwon-do, South Korea, has a small Cheonjin Harbor at its north end and a large Bongpo harbor to its south, as shown in Fig. 7. This crenulate-shaped beach, approximately 1.1 km long, is a Application of software MeePaSoL (Lee, 2015) developed to facilitate the use of the parabolic bay shape equation (Hsu and 280 Evans, 1989) indicates the beach is currently close to static equilibrium (using focus points B and C for the updrift and downdrift half of the beach shown in yellow curve, respectively; Fig. 7).
In geomorphic term, Bongpo-Cheonjin beach has received predominant waves from about N47°E direction (drawn by software MeePaSoL); whereas the prevailing wave direction in spring and summer is from N50°E and that in autumn and winter from N30°E in the open sea. Therefore, longshore sediment transport prevails from north to south in autumn and winter, especially 285 during high waves in winter, which had caused severe beach erosion (Fig. 8).

Sediment budget reduction in the study site
From a series of 10 aerial photographs of Bongpo-Cheonjin Beach (Fig. 9) spanning over 45 years from 1972to 2017(i.e., in July 1972, November 1979, October 1991, June 1997, May 2005, November 2010, May 2011, September 2013, November 295 2015, and July 2017, data of shoreline position, beach width, and area are extracted at three key locations (A, B, and C along the beach and marked on all sub-panels of Fig. 9 and values tabulated in Table 2). In addition, 37 sets of seasonal shoreline survey data collected during 2008-2017 and NOAA's wave data are applied, with the results presented are graphically in Sect.    Fig. 9 (MOF, 2018).  The beach width extracted from the aerial photograph is the value obtained by dividing the sandy beach area by the length of the shore at the time of the photographing. Therefore, depending on the incidence wave conditions at that time, it may not be able to reflect the effect of shoreline retreat caused by cross-shore sediment transport. The erosion width that occurs at a frequency of one year is about 16.3 m in the Bongpo-Cheonjin beach. It is judged that the range of changes in the beach width 310 in the aerial photograph is within the erosion width.

MM/YYYY
However, as shown in Fig. 10, since 1979.11, the beach area has been approximately 31,821 2 and the beach width has been maintained almost constant at about 28.9 . Although small underwater barrage was built on Cheonjin river located in the north, there are few the reduction potential in the sediment budget due to its small storage capacity. Then, the eroded beach width due to the sediment budget reduction potential to the beach width was also ignored as few. 315

Longshore sediment deposition potential caused by the construction of harbor breakwater
As shown in Fig. 11, the beach width of Bongpo-Cheonjin Beach appears to be remained at about 30 m for a long time between 2000 and 2017, in spite of the regional shoreline advance to form a static bay-shape after the construction of the Cheonjin Harbor breakwater. However, shoreline reshaping resulted in sediment deposition in the lee of breakwater and corresponding erosion in the other middle and south of the beach as given in Table 2. 320 The longshore deposition potential can be approximated by the bay-shape shoreline feature across the whole Bongpo-Cheonjin Beach (Fig. 11). First, the equivalent wave obliquity ( ) from the tip of the harbor breakwater can be approximated from the geometry of indentation ( ) in relation to the beach length ( ), The longshore sediment deposition potential is obtained by substituting the calculated with ′ , as indicated in Fig. 5 For a = 150 m (Fig. 11), Eq. (21) gives = 14,560 m 2 . The relationship between and ′ in Eq. (14) can be plotted as shown in Fig. 12 to obtain the dimensionless longshore sediment deposition potential ( 2 ) with values from 0 to 10. Alternatively, the value for / 2 can be obtained graphically from Fig. 12. By equating + with − (Fig. 11), the amount of beach erosion 330 width is estimated as 17 m by inputting the beach length from the breakwater ( = 850 m) into Eq. (15).

Cross-shore beach retreat due to the high wave incidence
Routine shoreline surveys have been conducted at least four times per annum for beaches in Gangwon-do, South Korea, since the 2000s. Specifically, a total of 37 sets of seasonal data were collected over 10 years from 2008 to 2017 for Bongpo-Cheonjin Beach. These data are plotted and fitted by a normal distribution (Fig. 13) to show local shoreline changes with standard 340 deviation of σ = 5.5 m. Figure 13 also compares alongshore distribution of the mean shoreline and retreated shoreline of 30year return period from statistical analyses ( =3.59). The beach width due to the cross-shore sediment retreat potential is evaluated as the value with the range from 5.57 to 23.16 (1 ≤ ≤ 100 ).

Erosion risk potential at Bongpo-Cheonjin Beach
The erosion risk potential is obtained by applying the ultimate beach erosion width by each erosion factor to the encroachment accumulation curve as given in Chapter 2. Figure 14 shows the encroachment accumulation curve according to the distance from the current average shoreline of Bongpo-Cheonjin Beach to the shore. Table 3 shows the encroachment area obtained for 350 each distance of 5m.
The erosion widths of sediment budget reduction potential and longshore sediment deposition potential are evaluated by 0 m and 17 m, respectively, thus representing the sum of individual components + of 17 m. And the cross-shore sediment retreat potential due to high waves is presented in Table 4. The results of shoreline retreat , consequence and risk potential for each return period are presented in Table 4, where the risk potential is calculated using Eq. (5). And 355 Figure 14 also shows the consequence per return period (1/ ), which are obtained using the encroachment accumulation curve, and figure 15 shows the variation of consequence and the erosion risk potential (ultimate erosion risk) with respect to return periods at Bongpo-Cheonjin Beach.

Discussion 370
In this study, a risk potential was introduced as the meaning of risk when an equilibrium state was reached for a long time, and a quantitative interpretation of risk potential was presented. That is, the risk potential, which is the planar area of the beach that can cause the maximum damage, is calculated excluding the continuous change of the shoreline with time scale. However, even if an erosion factor has occurred, it takes time for erosion to reach equilibrium state. And in order to properly understand the temporal change, it is required to identify more relevant coefficients depending on the target beach. Figure 16 shows the 375 approximate time scale difference in terms of beach width according to three different erosion occurrence elements.  First, shoreline retreat due to sediment budget reduction occurs as a result of source and sink imbalance in a long-term perspective over several decades. It shows the time-dependent change in the beach area by reflecting the effects of the sand 380 loss rate lost to the offshore and the decrease rate α of the sand flowing into the beach, which are variables representing the effects of source and sink. The theoretical solution is as follows (Lee and Lee, 2020).
where the sand loss rate is given as a constant value, and it is assumed that the beach area converges to (1 − ) due to the decrease rate α of the sediment discharge. Equation (20) shows that the beach area decreases rapidly at the beginning, but 385 converges to 95% or more equilibrium when time passes by 3 yr.
Secondly, the calculation of the erosion width due to longshore sediment transport can be estimated from empirical formulas such as the CERC equation (Shore Protection Manual, 1984). Starting from the angle difference between the initial and equilibrium shoreline angles at the boundary of erosion and deposition caused by shoreline deformation, the temporal width change is obtained by applying exponentially converging angle change to the formula for longshore sediment transport. 390 Here, is the ultimate beach width due to longshore sediment transport, and is the rate of change of angle according to time at the junction, and it is estimated by dividing the length of the beach and the vertical littoral height in the formula for longshore sediment transport. The equilibrium shoreline angle due to harbor or coastal structures is obtained based on the PBSE of Hsu and Evans (1989). 395 Finally, beach erosion due to the transport of cross-shore sediments is a short-term change that occurs over 20~40 days per a storm event. Shoreline retreats when high waves incidence and it recovers again when the wave is extinguished. Yates et al. (2009) confirmed that there is a linear relationship between the location of the shoreline converging to wave energy through field observation. Applying this recoverable process, the shoreline change model proposed by Miller and Dean (2004) can be expressed as the following ODE equation (Kim, 2021). 400 Here, is the beach recovery factor, and is the wave energy at the breaking point. And is a beach response factor between the wave energy and the mean shoreline. And another factor , which is proposed by Yates et al. (2009), has little effect, so it is excluded from Eq. (24). If only the value of the beach recovery factor , which has a unique value for each beach with different characteristics, is known, the temporal change of the shoreline according to wave energy can be estimated 405 using Eq. (24).

Concluding Remarks
This study presents a quantitative method for identifying the ultimate risk to beach erosion due to the anthropogenic development in watershed, coastal waters and lands, omitting climate change and sea-level rise. The sediment budget reduction potential caused by reduction in sediment supply from an upstream river was estimated using a principal of mass conservation 410 (Lee and Lee, 2020). The estimation of longshore sediment deposition potential was evaluated by the deformation of a static bay shape (Hsu and Evans, 1989). It is often caused by wave field changes after the construction of harbor breakwater, reclamation projects, and so on. Finally, the cross-shore sediment retreat potential by high/storm waves was estimated based on a statistical analysis of shoreline observation data.
The erosion consequence is obtained from the encroachment accumulation curve that accumulates the area to be damaged 415 by the hinterland development of the buffer section based on the average shoreline. Where the planar beach erosion potential obtained in advance is required to evaluate each consequence components. In addition, the erosion risk potential is estimated by multiplying the consequence and frequency. The frequency for and is considered as 1 −1 , on the other hands, that of is estimated from the statistical characteristics of shoreline survey data.
Through the case analysis for Bongpo-Cheonjin Beach of erosion grade D, Gangwon-do, South Korea, in which a coastal 420 maintenance project was recently conducted, the feasibility of methodology presented in this study was reviewed and the major risks of erosion were quantitatively identified. It was interpreted using a series of aerial photographs taken from 1972 to 2017 and survey data obtained from the erosion rating project started in 2010.
As a result, no dam was built in the watershed of the target beach, small-scale weirs were constructed, so the sediment budget reduction potential was judged to be insignificant enough to be difficult to quantitatively express. In addition, the longshore 425 sediment deposition potential was evaluated as 17 after the breakwater of Cheonjin harbor was extended by 40 . And the cross-shore sediment retreat potential was evaluated as the value with the range from 5.57 to 19.75 (1 ≤ ≤

30
). Therefore, if the shoreline retreat which is the sum of individual components is applied to the encroachment accumulation curve, the risk potential is obtained as the value with the range from 20.9 2 to 4969.4 2 (see Fig. 16 and Table 4). This means that erosion damage to 4,969.4 2 areas eroded at least once every 30 years can occur, requiring 430 engineering solutions such as setbacks or beach nourishment projects. https://doi.org/10.5194/nhess-2021-180 Preprint. Discussion started: 8 July 2021 c Author(s) 2021. CC BY 4.0 License.
The erosion risk potential was calculated by applying the standard deviation of 5.5m obtained from the shoreline survey data.
As a result, the peak risk potential of 357.54 2 occurred at 5 years recurrence. When the risk assessment method of this study is applied, therefore, it is possible to determine the optimal strategy, comparing the total risk obtained considering the actual damage cost for the erosion section with the average annual cost of the erosion reduction countermeasure method that reduces 435 the consequences or increases the return period.
The methodology proposed here enables the academic and quantitative identification of beach erosion risk and can help to devise engineering measures to eliminate or mitigate the causes of erosion. Although the case analysis of this study is limited, it is necessary to examine the feasibility of the proposed method by steadily applying it to other beaches with severe erosion and to improve it so that it can be applied to more beaches. 440

Data availability
Not applicable.