A Storm Hazard Matrix combining coastal flooding and beach erosion

Coastal storms cause widespread damage to property, infrastructure, economic activity and the environment. Along open sandy coastlines, two of the primary coastal storm hazards are coastal flooding by elevated ocean water levels and beach erosion as the result of storm wave action. At continental margins characterized by a shallow, wide continental shelf, coastal storms are more commonly associated with amplified storm surge and the damaging impacts caused by flooding of low-lying land. In contrast, along margins where the continental shelf is narrow and deep, coastal storm impacts are more often characterized by extensive beach erosion, due to the typically lower magnitude of storm surge but a higher proportion of deepwater wave energy reaching the shoreline. A new Storm Hazard Matrix is presented that integrates these two distinct but inherently linked open coast hazards. The approach is based on the combination of two hazard scales. The first is a ‘coastal flooding hazard scale’ that follows an established framework in which hazards are predominately driven by the vertical increase in ocean water levels during storms. The second is a storm wave ‘beach erosion hazard scale’ where hazards are predominately driven by the horizontal recession of the sandy beach and dune. The resulting framework comprises a total of nine unique combinations of flooding/erosion storm hazard regimes, from which six unified, qualitative indicators of the total storm hazard level ranging from ‘Low’ to ‘Extreme’ are defined. Real-world application of the Storm Hazard Matrix is explored at contrasting coastlines for two major storm events, encompassing an extratropical cyclone that impacted the coastline of southeast Australia in June 2016, and Hurricane Ivan that impacted the Gulf Coast of the United States in 2004. The new approach is shown to identify and distinguish between the severity of localized coastal flooding and/or coastal erosion, as well as provide enhanced insight to the nature, magnitude and alongshore variation of coastal storm hazards along the impacted coastline. Within the context of disaster risk reduction, preparedness and operational early warning, implementation of the Storm Hazard Matrix has the potential to deliver robust evaluations of storm hazards spanning a wider variety of both wave-dominated and surge-dominated coasts.


Introduction
There are few regions of the earth's surface more vulnerable to the damaging impacts of storms than the narrow strip of the coastal zone (Harley, 2018). Globally, storms rank as one of the deadliest 70 weather-related natural hazards (Whalstrom and Guha-Sapir, 2015). Coastal storms cause widespread damage to property, infrastructure, economic activity, and the environment. Along open sandy coastlines, beach and dune systems provide a first line of defence against the damaging impacts of the ocean. Two of the primary coastal storm hazards are coastal flooding by elevated ocean water levels (or 'storm surge') resulting in flooding of low-lying land; and beach erosion caused by storm 75 wave action. Individually or combined, both flooding and erosion pose a significant threat to settled coasts worldwide (Rueda et al., 2017;Mentaschi et al., 2018).
Understanding the nature and evolution of storm-induced coastal flooding and beach erosion is necessary to inform and enact appropriate and timely disaster preparedness (UNISDR, 2006). For example, coastal flooding as the result of ocean overtopping of wave overtopping and dune breaching 80 may escalate quickly within a matter of minutes to hours, leading to rapid inundation of potentially extensive areas of low-lying coastal land. Alternatively, storm wave beach erosion resulting in the undermining and failure of adjacent beachfront infrastructure, typically evolves progressively over comparatively longer timescales extending to hours and days. The differing nature of these coastal storm hazards also means that the impacts of erosion are generally restricted to the immediate vicinity 85 of the coast; with the post-storm natural recovery of the impacted beachfront typically spanning months to years (e.g. Morton et al., 1994;Phillips et al., 2019). This contrasts to coastal flooding of potentially much larger areas of land that more typically subsides in hours to days.
Coastal setting is a key factor that determines ocean hazards during a storm. Along continental margins characterized by a shallow, wide continental shelf, coastal storms are more commonly 90 associated with amplified storm surge and the damaging impacts caused by flooding of low-lying land.
In contrast, along margins where the continental shelf is narrow and deep, coastal storm impacts are more often characterized by extensive beach erosion, due to the typically lower magnitude of storm surge but a higher proportion of deepwater wave energy reaching the coastline. The relative contributions of these two hazards is therefore dependent on both the event-specific hydrodynamic 95 conditions (primarily wave energy and water levels) and the site-specific morphological characteristics of the impacted coastline (Harley et al., 2017).
Along open sandy coasts, storm-induced coastal flooding and beach erosion have the potential to be inherently linked, and it is therefore beneficial to consider them jointly (Pollard et al., 2019). As an illustration, prolonged storm wave attack over several consecutive high tides may progressively erode a dune sand barrier system. Once a threshold in dune depletion is reached, this may then trigger rapid and extensive coastal flooding as the defence provided by the dune is compromised. Understanding the interdependency of storm-induced coastal flooding and beach erosion is therefore important for assessing overall risk (Hillier et al., 2020).  (Dolan and Davis, 1992;Harley et al., 2017). In combination with these factors, the site-specific morphological setting is also important. Cliffed coastlines, for example, are more resistant to flooding and erosion, 110 while low-lying, sandy coastal barriers are more vulnerable. Given the complexity of the hydrodynamic and morphological factors involved in assessing coastal storm hazards, a conceptual framework that can be usefully applied to categorize the nature, magnitude and interaction of both potential hazards is beneficial. There are a range of existing approaches to categorize or quantify the severity of coastal flooding or beach erosion along open coasts due to storms. The most widely used categorical approach is the 120 'Storm Impact Scale' presented by Sallenger (2000). As is discussed further in the next section, this approach is based on four distinct 'impact regimes' that are defined by the vertical elevation of the maximum Total Water Level during a storm, relative to specific morphological features of the local beach and dune profile. Notably, storm wave energy is not considered directly in this schema. Several alternative approaches to calculating or ranking coastal storm impact severity also exist, based on 125 cumulative storm wave energy (e.g. Dolan and Davis, 1992;Harley et al., 2009;Mendoza et al., 2011), the cumulative storm tide residual (Zhang et al., 2002), or hybrid methods based on storm surge, wave height and/or storm duration (e.g. Kriebel et al., 1996;Miller and Livermont, 2009). Notably, with the exception of Sallenger (2000) all these approaches consider only the hydrodynamic conditions of a storm and do not consider the local subaerial beach and dune conditions. Another approach is to focus 130 only on storm impacts to dune systems and whether the integrity of this first line of defence is compromised (Judge et al., 2003;Armaroli et al., 2012).
Having established that elevated ocean water levels, storm waves and local morphology will all determine the ocean impacts of a storm along open sandy coastlines, and that coastal flooding and beach erosion are two distinct hazards that are also inherently linked, presented here is an integrated 135 Storm Hazard Matrix that aims to synthesise these multiple factors. Building from Sallenger's (2000) approach that is based on a vertical scale of storm impacts defined by elevated ocean water levels, a new horizontal dimension is introduced to explicitly include wave-induced beach erosion and its contribution to the total storm hazard. Application of the resulting Storm Hazard Matrix is explored along contrasting coastlines for two major storm events, encompassing an extratropical cyclone that

A combined coastal flooding and beach erosion hazard matrix
The new Storm Hazard Matrix developed and presented here integrates the two distinct but also inherently linked hazards of coastal flooding and beach erosion that occur along open sandy 150 coastlines. The approach combines two hazard scales: a 'coastal flooding hazard scale' that follows an established framework in which hazards are predominately driven by the vertical increase in ocean water levels during storms; and a storm wave 'beach erosion hazard scale', where hazards are predominately driven by the horizontal recession of the sandy beach and dune system. It is noted that for armoured coastlines, erosion hazards are likely to be less significant and other more suitable 155 approaches to categorizing the total storm hazard should be considered (e.g. Van der Meer et al., 2018). Alternative causes and mechanisms of coastal land flooding during storms -for example, rainfall resulting in increased water levels at the downstream boundary of rivers and estuaries -are also outside the scope of the framework presented.

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The characterization of coastal flooding hazards is adapted from Sallenger's (2000) well-known and widely-applied Storm Impact Scale. Originally developed to distinguish hurricane storm impacts along U.S. Atlantic and Gulf coast barrier islands, the Storm Impact Scale has since been used to characterize the impacts of storms at open coast beach and dune systems worldwide (e.g. Stockdon et al., 2007;Houser et al., 2008;Roelvink et al., 2009;McCall et al., 2010;Castelle et al., 2015). With this existing 165 framework as the starting point, the 'flooding hazard scale' used here is based on the same elevated ocean water level criteria and associated impact level regimes; however, the key difference is that an expanded range of morphological changes are considered separately by a second 'beach erosion hazard scale' (Section 2.2).
The Total Water Level (TWL) during a storm event is the vertical sum of astronomical tide, storm surge, 170 wave setup and wave runup. To distinguish four distinct storm impact regimes, Sallenger (2000) considered two representative high and low vertical TWL elevations associated with an individual storm; termed peak high TWL (ZTWL,high) and peak low TWL (ZTWL,low). Based on these upper and lower TWLs relative to the local elevations of the dune crest (Zcrest) and dune toe (Ztoe), the same terminology as Sallenger (2000) is now adapted to define four distinct coastal flooding hazard regimes, using the 175 following criteria: · Swash regime (ZTWL,high < Ztoe): This occurs when the peak high TWL does not reach the dune toe and therefore the swash is confined to the beach area. This represents the lowest level of coastal storm flooding hazard, with a safe corridor for access or amenity maintained between the dune and shoreline. 180 · Collision regime (Ztoe ≤ ZTWL,high): The peak high TWL is impacting the dune, resulting in the adjacent beach area being intermittently or continuously submerged. This represents the second level of flooding hazard, as a dry corridor between the dune and shoreline is now removed.
· Overwash regime (ZTWL,low ≤ Zcrest < ZTWL,high): This occurs when the dune crest is intermittently 185 overtopped. As a result, assets and property behind the dune may be subject to potential flooding. Flooding hazards may also be exacerbated during long-duration events or if inadequate drainage is provided.
· Inundation regime (Zcrest ≤ZTWL,low): The dune crest is constantly submerged. This represents the highest and most severe level of coastal storm flooding hazard for the open coast. 190 A schematic of these four coastal flooding regimes that are each based on vertical elevation criteria is presented in Figure 2 (left panel).

Beach Erosion -horizontal hazard scale
Beach erosion caused by the removal of sand from the beach and dune by storm wave action may be exacerbated by elevated ocean water levels (Pollard et al., 2019). However, this association between 195 higher TWL and larger waves, and their relative contribution to the total storm hazard, varies significantly along coastlines worldwide. To reiterate, factors such as the width and depth of the continental shelf control the local magnitude of storm surge and ocean wave energy that reaches the coast (Cohn et al., 2019;Serafin et al., 2019). To accommodate this, the approach adopted here is to first characterize these distinct hazards separately, then combine to determine their joint contribution 200 to the total storm hazard at any specific location.
To compliment the 'coastal flooding scale' outlined in Section 2.1, a second 'erosion hazard scale' is now developed. In contrast to the vertical elevation criteria used to define the four flooding hazard regimes, the definition of four new erosion hazard regimes is based on the horizontal and landward translation of key features of the beach and dune profile during a storm. Beach width change (ΔXwidth) 205 is defined as the change in the horizontal distance from the pre-storm dune toe to the shoreline, typically represented by a suitable elevation contour such as mean sea level or mean high water. A beach width change threshold (Xthreshold) then distinguishes between 'minor' and 'substantial' beach width narrowing. This threshold parameter is user-defined, so that it is adaptable and appropriate to a particular coastal setting or application. For example, a coastal researcher may choose to base this 210 threshold on the overall magnitude or percentage of horizontal shoreline change. In contrast, a coastal manager may define this threshold by the post-storm width of the beach relative to a coastal asset such as a building or a walkway. When the erosive action of storm waves extends landward to the dune, dune toe retreat (ΔXtoe) is defined as the change in horizontal distance at the elevation of the pre-storm dune toe. Finally, dune crest retreat (ΔXcrest) denotes the horizontal distance between the 215 pre-storm dune crest and the post-storm dune crest. This parameter indicates whether erosion and/or coastal flooding protection provided by the dune has been compromised.
Applying the criteria above, the resulting erosion hazard scale shown in Figure 2 (right panel) now categorizes four new beach erosion hazard regimes: · Minor beach narrowing regime (ΔXwidth < Xthreshold, ΔXtoe = 0): As the lowest level of beach 220 erosion hazard, the reduction in beach width does not exceed the user-defined threshold Xthreshold, and no changes to the dune system are observed.
· Substantial beach narrowing regime (ΔXwidth ≥ Xthreshold, ΔXtoe = 0): The reduction in beach width exceeds the user-defined threshold, but the dune remains intact. From a coastal management perspective, a suitable threshold can be selected so that this erosion hazard level will indicate 225 that the buffer provided by the beach is reduced, and the dune system may be vulnerable to subsequent storms.
· Dune face erosion regime (ΔXtoe < 0, ΔXcrest = 0): This occurs when sediment landward of the dune toe is eroded, but the dune crest is not impacted. Post-storm return of the dune buffer to pre-storm conditions may take of the order of months to years to fully recover. 230 · Dune retreat regime (ΔXcrest < 0): This represents the highest level of erosion hazard resulting in impacts to the landward side of the dune crest and any assets or other infrastructure that may be located in this area. If the dune crest is also lowered, then flooding hazards may be exacerbated. 235 Figure 2: Left: Coastal flooding (left) and beach erosion (right) hazard scales and the criteria used to distinguish between individual hazard regimes. Peak high TWL (ZTWL,high) and peak low TWL (ZTWL,low) are respectively defined as the representative high and low water levels and include the effects of astronomical tides, storm surge, wave setup and wave runup. The pre-storm dune is parameterized by two features: the dune crest elevation (Zcrest) and dune toe elevation (Ztoe). The change in beach width (∆Xwidth) is defined by the change in horizontal distance between the pre-storm dune toe position 240 and shoreline. The beach width threshold (Xthreshold) is a user-defined threshold defined as a horizontal distance from the pre-storm shoreline position. Changes to the dune toe position (∆Xtoe) and dune crest (∆Xcrest) position are defined by the horizontal distance between the pre-storm and post-storm dune toe and crest respectively.

Combined Storm Hazard Matrix
The Storm Hazard Matrix shown in Figure  Once storm events reach this severity, complex feedback loops between flooding and erosion hazards are more prevalent (e.g. dune crest lowering causing further flooding) and active hazard mitigation actions by the coastal manager are likely to be warranted.
· Severe storm hazard level: When overwash and dune retreat regimes are occurring simultaneously, the area behind the dune may be at exacerbated risk of both erosion and flooding hazards. The exposure and vulnerability of coastal assets may warrant a significant emergency response.
· Extreme storm hazard level: Combination of the two end-scale inundation and dune retreat 280 flooding and erosion hazard regimes has the greatest potential to cause major damage at the coastline. This threat would be of the highest concern to coastal managers, and likely require extensive pre-storm preparedness, implementation of hazard mitigation measures and poststorm recovery operations across the impacted areas. and their distribution alongshore. The extratropical low pressure event in SE Australia was characterized by prolonged, high energy wave conditions along an embayed coastline that exhibits a 300 narrow and deep continental shelf, primarily resulting in beach erosion hazards observed (Harley et al., 2017). In contrast, the Hurricane Ivan event in NW Florida was associated with high storm surge that primarily exposed the linear, low-lying, barrier island system located in the shallow coastal region of the Gulf of Mexico, to coastal flooding hazards (McCall et al., 2010;Plant and Stockdon, 2012). The differing regional settings and storm characteristics of these two events are outlined below, resulting 305 in quite different outcomes when the Storm Hazard Matrix is applied.

Regional settings, storm characteristics and coastline impact observations
Between 4-7 June 2016 an intense extratropical storm (known locally as an 'East Coast Low') impacted more than a 1000 km of the southeast Australia coastline. The region considered here that is located in the state of New South Wales (NSW) is characterized by embayed sandy beaches separated by rocky 310 headlands. Exacerbated storm impacts were observed due to the anomalous easterly direction of the storm combined with the coincidence of the storm peak with highest astronomical tides. Immediate pre-and post-storm aerial LIDAR surveys of approximately 178 km of sandy beaches between Sydney and Coffs Harbour were conducted (Figure 4a). Using these datasets, pre-and post-storm beach and dune transects were extracted at every 100 m alongshore. Wave conditions at the 10 m isobath at 315 each transect were estimated using multiple, nested WAVEWATCH III models while still water levels (i.e., astronomical tide + storm surge) were recorded by five tide gauges across the region. An example wave timeseries, water level timeseries and pre-storm transect are shown in Figure 4c, Figure 4d and (2010) and Plant and Stockdon (2012).

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Differences in the morphological setting and hydrodynamic conditions between the two regional locations and these two storm events are apparent in Figure 4. While maximum wave heights during the two events were quite similar, the NSW coastline was subjected to a substantially longer duration of high energy storm wave conditions (Figure 4c). At Santa Rosa Island elevated water levels at the peak of the storm were exacerbated by pronounced storm surge that increased then subsided 340 relatively quickly (Figure 4d). Along the NSW coastline, storm surge was relatively minor; the coincidence of the storm with highest astronomical tides was the main driver of elevated water levels.
The pronounced differences in the morphological setting of the two regions is demonstrated in Figure   4e. Santa Rosa Island is typical of linear, low-lying barrier island systems on the U.S. East and Gulf coasts that experience large storm surges (Zhang et al., 2002). The embayed NSW coastline on the 345 other hand, generally consists of a more substantial barrier dune system with the occurrence of storm surge limited by the region's steep and narrow continental shelf (McInnes and Hubbert, 2001).
Using the available 100 m alongshore beach and dune profiles, the pre-and post-storm dune toe and dune crest positions were identified manually, then compared to the local waves and water levels at each transect to classify the erosion hazard regime at every 100 m alongshore. The cross-shore 350 position of the shoreline at mean high water level was selected to determine pre-and post-storm beach width. For the purpose of illustration, a 30% change relative to the pre-storm beach width was adopted as the threshold criteria to distinguish between 'minor' and 'substantial' beach narrowing. This is of course arbitrary, and as previously noted in Section 2.3, this threshold condition is defined by the user so that it best suits a location-specific management and/or research application. Since no 355 direct TWL observations during either event were obtained, flooding hazard regimes at each transect were estimated by summing the tide and measured (NSW) or modelled (Santa Rosa) storm surge ( Figure 4d) with an empirical estimate for combined wave setup and runup, using the widely-used model of Stockdon et al. (2006). The peak high TWL and peak low TWL (refer Section 2.1 and Figure 2) were estimated at each transect based on the 2% runup exceedance. Adapting the approach outlined 360 in Stockdon et al. (2007), classification of the coastal flooding regimes for every 100 m alongshore transect were obtained.

Comparison of Storm Hazard Matrix classification
A synthesis is presented in Figure 5 that shows the occurrence of each of the coastal flooding and beach erosion hazard regimes, as well as the relative prevalence of each resulting storm hazard level 365 for the NSW 2016 and Santa Rosa 2004 coastal storms. For the NSW event, the most common storm hazard level is high (47%), which combined with moderate (29%) and low (20%) accounted for 96% of the total region. In contrast, for the Santa Rosa event the great majority of the hazard level is severe (72%). While both events were considered to be a serious threat to their respective communities, the higher storm hazard levels at Santa Rosa Island match the extensive damage to property and 370 infrastructure that was reported for this event (DEP Florida, 2004), compared with NSW where impacts were observed to be much more localized (NSW DJOEM, 2016).
Separately examining the flooding and erosion hazard regimes for both these events ( Figure 5, left and middle panels) provides additional insight. For example, at the regional scale, storm hazard levels predominantly in the range of low to high occurred along the NSW coast during the 2016 ECL event 375 and were primarily the result of beach narrowing and dune face erosion. Contrasting to this, the very high to extreme storm hazard levels along Santa Rosa Island during Hurricane Ivan were associated with coastal flooding hazards as the result of dune overwash. Additionally, the Storm Hazard Matrix approach can usefully distinguish within the single collision flooding regime between the quite distinct hazard levels of high (dune face erosion) and very high (dune retreat).

Synthesis and future directions
The Storm Hazard Matrix summarized in Figure 3 applied in the previous section to two contrasting 420 storm events along very different coastal settings in Australia and the USA, demonstrates the potential utility and benefits of assessing coastal flooding and beach erosion hazard regimes within a single framework to categorise an integrative storm hazard level. A particular advantage of this approach is that no initial assumption is necessary of the relative dominance of coastal flooding versus coastal erosion. For the case of significantly elevated Total Water Levels relative to lower dune heights that 425 would result in the predominance of coastal flooding hazards, the Storm Hazard Matrix encapsulates the existing Sallenger (2000) 'Storm Impact Scale'. However, for more elevated dune systems along coastlines where energetic storm waves cause greater impact than the associated storm surge, practical experience is that beach and dune erosion hazards dominate, that are not sufficiently captured by a TWL-based approach alone. Importantly, separately classifying the flooding (vertical) 430 and erosion (horizontal) hazard regimes can provide additional insight by distinguishing between the severity of localized impacts. As illustrated in Figure 5  In the broader context, categorising and distinguishing storm hazards that threaten sandy coastlines is well recognized as an essential step in natural disaster risk reduction, informed decision-making and coordinated mitigation actions (Weichselgartner and Pigeon, 2015). The Sendai Framework for Disaster Risk Reduction (UNDRR, 2015) recommends several actions for countries to prioritize, which include understanding disaster risk and enhancing disaster preparedness for effective response. 440 Present efforts around the world on applying these approaches to reduce the risk of coastal disasters (e.g. van Dongeren et al., 2018) has identified that additional tools are needed. The Storm Hazard Matrix proposed here is one approach that can now be applied as a practical tool to distinguish and categorize coastal hazards within the context of strategic planning and risk assessment.
In parallel to this, there is a growing focus and effort internationally on early warning along coastlines 445 that are impacted by damaging coastal storms (Ciavola et al., 2011;Barnard et al., 2014;Ciavola and Coco, 2018;van Dongeren et al., 2018). Operational early warning systems (EWS) with a typical 7-day forecast lead time all require careful consideration of an appropriate hazards classification and ranking scale that is suitable to inform emergency preparedness and public safety warnings. In particular, it is a priority to establish efficient, practicable methods that can be readily applied to forecast localized 450 hazards spanning regions of several 100's km of coastline. At the present time, more complex and physics-based numerical modeling approaches are computationally prohibitive for this purpose.
Application of the Storm Hazard Matrix in this context of operational EWS is a current focus of active investigation.
While the relative simplicity of the Storm Hazard Matrix developed and presented here results in an 455 approach that can be readily adopted across differing coastal regions, it is necessary to recognise that this is predicated on the availability of morphological and hydrodynamic information. In particular, up-to-date beach and dune topography is a requirement, especially for dynamic beach and dune systems where antecedent morphological conditions are crucial to determining storm impacts (Beuzen et al., 2019b). Encouragingly, the regular collection of airborne Lidar of the more slowly 460 evolving back-beach and dune area is becoming increasingly routine for many coastal regions around the world (e.g. Sallenger et al., 2005;Zhang et al., 2005;Middleton et al., 2013;Burvingt et al., 2016;Kim et al., 2017). Combined with more recent advances in the use of satellite-derived methods to rapidly determine the pre-storm position of the shoreline (i.e., beach width) and beach face slope (e.g. Vos et al., 2019), the near real-time integration of these sources of beach and dune topographic 465 information is presently being explored. Similarly, Several global models (e.g. NOAA Wavewatch III, Deltares Global Flood Forecasting and Information System, Aviso Global Tide FES model) can provide deepwater wave, tide and surge information along coastlines where these are not measured locally, however the estimation of wave setup and runup is still likely to be dependent on calculations of sitespecific wave transformation in the nearshore (da Silva et al., 2020). Probabilistic methods such as 470 ensembles (Beuzen et al., 2019a), Monte Carlo (Davidson et al., 2017) and Bayesian networks (Beuzen et al., 2018) are practical approaches that enable uncertainty in local morphology and storm hydrodynamics to be appropriately considered. As the availability of routine coastal observations spanning regional scales continues to expand and modelling tools improve, implementation of the Storm Hazard Matrix within the context of operational Early Warning Systems has the potential to 475 deliver forecasts of coastal storm hazards spanning both wave-dominated and surge-dominated coasts.