Compound coastal flood risk in a semi-arid urbanized region: The implications of copula choice, sampling, and infrastructure

. Sea level rise will increase the frequency and severity of coastal flooding events. Compound coastal flooding is characterized by multiple flooding pathways (i.e., high offshore water levels, streamflow, energetic waves, precipitation) acting concurrently. This study explores the joint flood risks caused by the co-occurrence of high marine water levels and precipitation in a highly urbanized semi-arid, tidally dominated region. A novel structural function developed from the multivariate analysis is proposed to consider the implications of flood control infrastructure in compound coastal flood risk assessments. Univariate 5 statistics are analyzed for individual sites and events. Conditional, and joint probabilities are developed using a range of copulas and sampling methods. The Independent, and Cubic copulas produced poor results while the Fischer-Kock, and Roch-Alegre generally produced robust results across a range of sampling methods. The impacts of sampling are considered using annual maximum, annual coinciding, wet season monthly coinciding, and wet season monthly maximum sampling. Although , annual maximum sampling is commonly recommended for characterizing compound events, this work suggests annual maximum 10 sampling does not produce ““worst-case” (cid:58) ” (cid:58) event pairs and substantially underestimates marine water levels for extreme events. Wet season coinciding water level and precipitation (cid:58)(cid:58)(cid:58)(cid:58)(cid:58)(cid:58)(cid:58)(cid:58) sampling pairs benefit (cid:58) s from a dramatic increase in available data (cid:58)(cid:58)(cid:58)(cid:58) data (cid:58)(cid:58)(cid:58)(cid:58) pairs, improved goodness of fit statistics, and provide a range of physically realistic pairs. Wet season coinciding sampling may provide a more accurate compound flooding risk characterization for long return periods in semi-arid regions.


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Coastal flooding is a significant human hazard Wahl et al., 2015) and is considered a primary health hazard by the U.S. Global Change Research Program (Bell et al., 2016). Coastal migration and utilization continues to increase (Nicholls et al., 2007;Nicholls, 2011). Over 600 million people populate coastal zones (Merkens et al., 2016). Climate change induced ::::::::::::: change-induced sea level rise will substantially increase flood risk (Church et al., 2013;Horton et al., 2014), and negatively impact coastal populations (Bell et al., 2016). Even relatively modest sea level rise will significantly increase flood 20 frequencies through the US (e.g., Tebaldi et al., 2012;Taherkhani et al., 2020). Southern California is particularly vulnerable to sea level rise. Small changes in sea level (∼5 cm) double the odds of the 50-year flooding event (Taherkhani et al., 2020) and the 100-year :::::::: 100-year event is expected to become annual by 2050 (Tebaldi et al., 2012). Regional research has explored flood risks caused by sea level rise and coastal forcing (e.g., Heberger et al., 2011;Hanson et al., 2011;Gallien et al., 2015). nual maximum sampling and select a secondary variable which co-occurs with the primary variable (Lian et al., 2013;Xu et al., 2014;Tu et al., 2018), creating a "coinciding" type sampling. Multivariate applications relying upon annual maximum sampling generate a "worst case" scenario which may produce unrealistic variable combinations. Coinciding sampling draws from physically realistic event pairs. Although, multiple studies explore sampling effects on fitted distribution parameters and univariate return periods (Engeland et al., 2004;Jarušková and Hanek, 2006;Peng et al., 2019;Juma et al., 2020), sampling effects for multivariate coastal flooding events is unknown.
Coastal flooding studies primarily focus on locations defined by storm surge dominated oceanographic conditions with warm, humid (Wahl et al., 2012;Lian et al., 2013;Xu et al., 2014;Masina et al., 2015;Wahl et al., 2015;Mazas and Hamm, 2017;Paprotny et al., 2018;Tu et al., 2018;Bevacqua et al., 2019;Didier et al., 2019;Xu et al., 2019;Yang et al., 2020), and monsoonal (Jane et al., 2020) climatic conditions. In contrast, along the southern California coast typical tidal variability is 1.7 to 2.2 m (Flick, 2016) and storm surge rarely exceeds ∼20 cm (Flick, 1998). Notably, during the wet season (October to 70 March), when precipitation typically occurs, spring tide ranges are relatively large (∼ 2.6 m). Critically, few studies consider areas where coastal flooding events are dominated by large tides and either precipitation or wave events (Masina et al., 2015;Mazas and Hamm, 2017;Didier et al., 2019;Jane et al., 2020). This study explores univariate and multivariate flooding events in a semi-arid, tidally dominated, highly urbanized region. Here, the dependency between observed water levels and precipitation, impacts of sampling methods and distribution fitting, and the most likely flood values are explored. semi-arid, tidally dominated sites in the US. All are low-lying estuarine or bay-backed highly urbanized beach communities requiring extensive coastal management to mitigate flooding events. For example, sea walls and artificial berms in 80 Sunset Beach protect infrastructure from high embayment water levels, wave runup, and overtopping along the open coast. The storm drain network is managed to prevent back flooding during high tides. Notably, Gallien et al. (2014) suggested when tide valves are closed, the storm drain network cannot remove ::::: reduce : pluvial flooding caused by alternative flooding pathways (e.g., precipitation or wave overtopping). Pacific Coast Highway (PCH) is heavily utilized and is a primary transportation corridor along the southern California coastline. All locations are densely urbanized and highly impacted by flooding.
The U.S. Hourly Precipitation Data dataset provided by NOAA's National Centers for Environmental Information (NOAA, Accessed 2021c) at the Signal Hill (COOP:048230), Los Angeles International Airport (COOP:045114), and San Diego Inter-100 national Airport (COOP:047740) stations is used as the precipitation inputs. Observations do not contain trace amounts (< 0.25 mm) and is :: are : provided as cumulative precipitation (mm) per event. Precipitation measurements were converted to a mm/hr rate :: by :::::::: dividing ::: the :::: total :::: event ::::::::::: precipitation :: by ::: the ::::: event :::: time : to match the hourly OWL measurements. The final precipitation input is a 24-hour cumulative precipitation record made from the hourly observations. All data was transformed to UTC for analysis.
Distributions are fit with existing precipitation observations greater than zero consistent with previous studies (Swift Jr and Schreuder, 1981;Hanson and Vogel, 2008). Months with no OWL measurements were also excluded. In the case of coinciding 120 sampling, pairs that had three or more OWL measurements missing within the 24-hour window were manually reviewed and removed if the ::: their : tidal peak was clearly missing. Specifically for WMM sampling, months with more than half its :::: their observations missing were also reviewed and removed if the tidal peak was missing. The resulting data pairs are shown in Fig.   2.   Potential flooding events are determined with three different probability definitions: univariate, conditional, and bivariate. Assuming X and Y are random variables, x and y are observations of these variables, and F X and F Y represent the variables' respective cumulative distribution functions (CDF). Formulations for univariate (F X (x), F Y (y)) and bivariate joint (F XY (x, y)) CDFs follow DeGroot and Schervish (2014) (Eq. (1) and (2)). Conditionals (F X|Y ≥y (x|Y ≥ y), F X|Y ≤y (x|Y ≤ y), and  (4) and (5)). Conditionals 1 (C1), 2 (C2), and 3 (C3) represent Eq. (3), (4), and (5) going forward. Univariate statistics are developed using the appropriate continuous random variable distribution while conditional and bivariate CDFs are determined using copulas.
Copulas are functions that associate random variables' univariate CDFs to their joint CDF (e.g., F X and F Y to F X,Y (x, y)) according to Sklar's theorem (Sklar, 1959;Salvadori, 2004). There is no requirement for the univariate distributions to be 135 the same. This is particularly advantageous since the optimal univariate distributions may be used for each variable. Bivariate probabilities for different hazard scenarios, which represent various multivariate events, and conditional probabilities can be calculated using fitted copula functions.

Hazard scenarios
Notation and definitions from Salvadori et al. (2016), unless otherwise stated, is ::: are used to define the upper set (S) and scenario 145 types. Salvadori et al. (2016) and Serinaldi (2015) present figures of each scenario's probability space. Further discussion of hazard scenarios and copulas assume a bivariate situation.

"OR"
"OR" scenario events have one or both random variables exceed a specified threshold. That is, what is the probability of a water level or precipitation event exceeding a given value? Standard univariate CDFs make up the associated copula.

"AND"
"AND" scenario events have both random varibles exceed a specified threshold. In this case the fundamental question is "what is the probability of a particular water level and precipitation rate exceeding specified values?". The survival copula (Ĉ(u, v)) is comprised of univariate survival CDFs (F(x) = 1 − F(x)) and the provided equation can be found in Serinaldi (2015) and 155 Salvadori and De Michele (2004).
"Survival Kendall" (SK) scenario highlights an infinite set of AND events which also separate safe and dangerous statistical spaces. AND events along a t also share a common probability, but define separate regions. Events along an SK t represent the same super critical region, but provide an "(upper) bounded safe region" (Salvadori et al., 2013). The Survival Kendall 170 specifically considers the largest AND events of concern and is estimated by the method outlined in Salvadori et al. (2013).
In this work, the structural failure functions :::::: function : focuses on the question "what is the probability of a water level forcing tide valve closure and subsequent flooding during a precipitation event?". Raftery, Shih-Louis, Linear-Spearman, Fischer-Hinzmann, Husler-Reiss, Cube, and Marshal-Olkin copulas do not have a PDF function. A PDF is required to determine the most likely value along an isoline, therefore removing : it ::: was ::::::: decided :: to ::::::: remove those copulas from the study. Copulas must also be computationally simple to derive or integrate to calculate Conditional 3.

Return periods
Hydrologic events are commonly cast in the context of return periods (e.g., De Michele et al., 2005, 2007FEMA, 2011;Wahl et al., 2012;USACE, 2013;Salvadori et al., 2014;Wahl et al., 2015;Salvadori et al., 2015). Return periods (T ) provide an easily interpreted metric describing the severity of an event and is the inverse of an event's probability of exceedance presented as F in Eq. (14) (Tu et al., 2018). In Eq. (15), N is the data's time window, n is the number of considered events within N , 195 and N e is the average number of events per unit of time (monthly, yearly, etc.). Therefore, N e = 1 when considering singular events within a year (Tu et al., 2018).
N e = n/N 3.5 Goodness of fit metrics

Results
Univariate, conditional, and bivariate probabilities were developed using four sampling methods (AC, AM, WMC, WMM) and seventeen different copulas. Figure 3 presents marginal distribution results for all sites and sampling. Two marginal distributions do not pass the chi square test at the standard 0.05 level of significance (San Diego AM OWL and Santa Monica WMM OWL).

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These distributions pass at reduced significance levels of 0.01. Additionally, Santa Monica's AM data is slightly negatively correlated (> −0.06). Copula and sampling effects differ significantly at low (i.e., low return period) and high (i.e., severe return period) probabilities of non-exceedance. In the case of annual sampling, non-exceedance (exceedance) probabilities are 0.9 (0.1) and 0.99 (0.01) for the 10-and 100-year events, respectively. In wet season sampling, return period exceedance probabilities vary depending on sampling type and location due to the average number of event observations per year (N e from 220 Eq. (15)). For example, San Diego WMC sampling has 329 observations within the 65 year record (i.e., N e = 5.06). Therefore, the exceedance probabilities (F in Eq. (14)) associated to a 10-and 100-year event are 0.0198 and 0.0020 (non-exceedance probabilities at 0.9802 and 0.9980), respectively. Table 3 presents wet season (WMM and WMC) exceedance probabilities for all sites. The selected marginal distributions (Fig. 3, Table 4) were tested and/or suggested fits in previous studies. Rainfall has been widely fit with an Exponential distribution (refer to Table 2 in Salvadori and De Michele (2007)), but more recently been fit using a variety of distributions including Gamma (Husak et al., 2007), Rayleigh (Pakoksung and Takagi, 2017;Esberto, 2018), Generalized Pareto or Birnbaum-Saunders (Ayantobo et al., 2021). In the case of annual precipitation sampling (coinciding or maximum) Santa Monica was well described by a Birnbaum-Sanders, Rayleigh best described Sunset data, and a Gamma was 230 the best fit for San Diego data. Similarly, wet season precipitation data (maximum or coinciding) was best described by the Exponential distribution for Santa Monica and Sunset while the Generalized Pareto best represented San Diego.

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Observed water levels did not exhibit site specific patterns and were described by a range of distributions (Table 4).

Copulas
The quality of a copula's fit is determined by its maximum likelihood (ML) values. Figure 4 presents ML values for the 17 tested copulas at each site (columns) per sampling method (rows). Fits produced similar ML statistics for a given site and sampling method, however, a few copulas produced particularly poor or unusual results. For example, the Independent and Cubic were 240 consistently ranked as the lowest fit. Additionally, a number of copulas generally perform well (Fig. 4). For example, the Fischer-Kock (Fisc.), Tawn, and Roch-Alegre (Roch.) were amongst the better fitting copulas, ranking within the top five ML for nearly all datasets. The Tawn has previously been used in a OWL and precipitation analysis (Jane et al., 2020) and in this case, is frequently the highest ranked. All other copula results were within the envelopes described by the five copulas. Unless otherwise noted, these focused copulas will be used to consider the impacts of copula choice and sampling.

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San Diego WMC conditional CDFs display the impacts of individual copulas :::::::: individual ::::::: copulas :::::: effects (Fig. 5). The Independent and Cubic copulas consistently suggest lower OWL (Fig. 5a, e) and precipitation values (Fig. 5b, f) while, in this example, the Tawn suggests substantially higher OWL and precipitation values (dashed line, Fig. 5a, b, e, f). C1's 100-year pair in Table 6 displays an example of the Tawn's conservative nature. The Roch-Alegre and Fischer-Kock provide highly consistent ::: very :::::: similar : results for both precipitation and water level (black and green lines, Fig. 5a, b, e, f). Copula choice 250 has nearly no effect on the Conditional 2 scenario (Fig. 5c, d). Most probable OWL and precipitation values in Tables 5 and   6 further display the aforementioned behaviors. These conditional patterns generally persist at all locations with an additional note that the Tawn, Roch-Alegre, and Fischer-Kock copulas typically provide similar results. Figures 6 and 7 show the 10-and 100-year return periods, respectively, for the five focused copulas using WMC sampling at SD. In all the hazard scenarios, the Independent and Cubic copulas suggest most probable events dominated by either large 255 precipitation or OWL ( Fig. 6 and 7). For example, AND 100-year OWL is unrealistically small compared to the other OWL values provided by alternative copulas (Table 6). Clearly the Tawn presents conservative results suggesting higher OWL and precipitation pairs in the AND scenario ( Fig. 6a and 7a precipitation pairs while the Roch-Alegre and Fischer-Kock suggest the moderate OWL and precipitation levels ( Fig. 6c and   260 7c). The OR and Kendall scenarios suggest quite similar isolines with the most probable precipitation varying between copulas ( Fig. 6b, d, and 7b, d). Tables 5 and 6 further display the bivariate patterns. Again, these bivariate patterns generally persist at all locations with an additional note that the Tawn, Roch-Alegre, and Fischer-Kock, copulas often generate similar values.      Fig. 8a, c, e), where as :::::: whereas : wet season samplings exhibit similar precipitation CDFs (red and black lines Fig. 8b, d, f). OWL values are generally larger for maximum sampling at lower non-exceedance probabilities (i.e lower return periods) (Fig. 8a, c, e blue and black lines, Table 7). However, the extended tail from WMC sampling produces larger OWL at higher return periods (red line Fig. 8a, c, e; Table 8). Annual coinciding sampling displays significantly lower OWL values at low (Table 7) and high (Table   270 8) return periods. Only minimal differences between annual and wet season precipitation exist at the 10-and 100-year return periods (maximum difference of 1.79 and 3.08 mmday −1 respectively; Tables 7 and 8). Annual (wet season) precipitation CDFs appear similar as OWL measurements are chosen subsequent to precipitation observations (Fig. 8b, d, f).
Figures 9 and 10 present the 10-and 100-year return periods using the Fischer-Kock copula for all samplings (AC, AM, WMC, WMM). For the AND and K scenarios, AM sampling results in the largest OWL compared to the other sampling 275 methods (Fig. 9a, d and 10a, d, Tables 7 and 8). Additionally for the AND and K scenarios (Fig. 9a, d and     precipitation events without regard to co-occurrence. For example, in the 10-year return period AM OWLs are at least 30 cm 285 higher than AC (Table 7). In the 100-year return period AM exceeds AC by at least 17 cm (Table 8). Precipitation is generally consistent across all conditionals, scenarios and sampling types with only minor variations observed. The AND scenario is the exception to this where substantially lower precipitation values are seen across all sampling and and scenarios. AM and WMM

Structural failure
A unique structural scenario is presented to consider flood severity along the Pacific Coast Highway (PCH) in Sunset Beach.
PCH road elevation ranges from 1.7-2.4 m NAVD88 (Fig. 11), below typical spring tide (∼2.13 m) and more extreme (∼2.3 m) water levels (NOAA, Accessed 2021b), requiring tide valves along PCH for flood prevention. Tide valve closures prevent back-flooding from high bay water levels coming up through subsurface storm drains that (normally) discharge to the bay.

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Additionally, closed tide valves also enable precipitation pooling since water cannot be drained to the bay. Severe pooling may result in a critical highway closure, which can further damage property and inhibit emergency service operations.
Areal precipitation flooding extent and depth can be estimated for water levels exceeding tide valve closure elevation. A water level equal :: to or greater than 1.68 m NAVD88 forces valve closures and frames the structural failure as a Conditional 1 Figure 11. Elevations within the PCH boundary ranging from low (purple) to high (blue).Background imagery from NOAA (Accessed 2021a).
type event. The local watershed is convex and drains an area of 94,897 m 2 . Water pools in the low elevation areas along PCH 300 (Fig. 11). When pluvial water levels exceed the sea wall elevation, water overflows the sea wall and exits to the harbor. The maximum pool storage is 11,342 m 3 . The percent of flooding is then calculated with Eq. (20) as the structural function.
Structural scenario precipitation and percent flooding (Ψ) values utilizing the Roch-Alegre, Fischer-Kock, and Tawn copulas are shown in Table 9. Rows and columns separate the utilized sampling methods and return periods of interest, respectively. Fig.   12 shows Ψ as a function of precipitation for the Roch-Alegre, Fischer-Kock, and Tawn copulas along with the 5-(square), 10-305 (circle), and 100-year (diamond) return periods. All copulas display similar values across sampling methods with the exception of the Tawn, which presents more conservative values using WMC sampling (Fig. 12, Table 9). For example, the 10-year WMC for the Tawn (Fig. 12c) is over 80 percent flooding compared to approximately 70 percent with the other copulas. Again, AC sampling severely underestimates precipitation and flooding.

Discussion
Previous multivariate studies typically use a small, popular group of copulas (e.g., Clayton, Frank, Gumbel, Student t, and Gaussian). Gaussian and Student t copulas were excluded :::: from ::: this ::::: study : due to their lack of a computationally simple derivative or integral while the Clayton, Frank, and Gumbel generally provided average fits (Fig. 4). Tawn, Fischer-Kock, and Roch-Alegre copulas generally present similar values with the Tawn occasionally presenting more conservative pairs (Fig. 7). Cubic and The poor performance of the Independent copula further emphasizes the importance in accounting for dependencies between variables in multivariate studies (Raynal-Villasenor and Salas, 1987;Yue and Rasmussen, 2002;De Michele et al., 2005).
Well fit copulas concentrate probabilities around more centralized intermediate OWL and precipitation values for compound events. This is most pronounced at higher (i.e., 100-year) return periods (Fig. 7)). Given that nearly all copulas, save the Cubic, 320 Independent, and Tawn, exhibit similar ML values (for a given sampling) suggests that choosing a reasonable copula may be sufficient to provide a robust characterization of considered compound flooding events.
The choice in sampling imparts a significant influence on flood risk interpretation. Substantially lower ML values are observed in annual sampling (Fig. 4a-f) compared to wet season sampling (Fig. 4 g-i). This likely results from the the increased data availability when the entire wet season is used compared to a single annual observation. When maximum versus coin-325 ciding sampling is considered, maximum samplings (AM and WMM) tend to provide the largest OWL at low return periods ( Fig. 8a, c, e, Fig. 9, and Table 7). At larger return periods, WMC then provides significantly larger OWLs (Fig. 8a, c, e, Fig.   10, and Table 8). This is observed in the conditionals and bivariates (minus the AND and K hazard scenarios which maximum samplings display the largest OWLs) at all sites. From a logical perspective, coinciding sampling provides a more realistic view of compound events (by definition these are pairs that have co-occurred to produce a compound flooding event). At long 330 return periods AC sampling may require a long data record, which is often unavailable. Notably, in this study AC produced Table 9. Precipitation and percent flooding (Ψ) associated to the 5-, 10-, and 100-year return periods (T ) using the Roch-Alegre, Fischer- OWL samplings that were substantially lower than any of the other samplings. For example when comparing 100-year OWLs with AC and WMC samplings, the marginal was 32 cm lower and the AND scenario was 17 cm lower (Table 8). Given that sea wall protected urban coastal areas are highly sensitive to even minor elevations differences (e.g., Gallien et al., 2011), this suggests with limited data records AC sampling should be avoided.

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An important note is each probability type appropriately describes a unique event, characterized by OWL and precipitation.
Serinaldi (2015) suggests inter-comparing univariate, multivariate, and conditional probabilities and return periods is misleading as each probability type describes its associated event. Events where only extreme OWL or precipitation is of concern, should simply utilize marginal statistics and follow current FEMA guidelines. Compound event analysis may utilize a variety of scenarios. Conditional type distributions become useful when future information on one variable is known (ex., predicted 340 OWL levels). AND scenarios may be applied when both variables exceeding given limits is of concern. The Survival Kendall scenario is an alternative to the AND scenario using a more conservative approach to develop events of concern (Salvadori et al., 2013). An OR scenario should be applied when either compounding variable exceeding a limit is of concern, whereas the Kendall scenario provides minimum OR events of concern (Salvadori et al., 2011).

The benefit of the Kendall and Survival
Kendall is all the events along their isolines describe a similar probability space versus the AND and OR isolines describe 330 345 events with similar probabilities of non-exceedance. The majority of previous studies focus on specific probability types and do not consider multiple flooding pathways. Only a single study explores all the probabilities associated to different extreme events (Serinaldi, 2016).
From a regulatory perspective, FEMA recommends individual (univariate) analysis to develop return periods for compound coastal flooding applications (FEMA, 2011(FEMA, , 2016c(FEMA, , 2020, and blending the two hazard mapping results. Fundamentally, this 350 type of approach assumes (event) independence and may underestimate compound flood hazards (e.g., Moftakhari et al., 2019;Muñoz et al., 2020). FEMA provides guidelines for coastal-riverine (FEMA, 2020), tide, surge, tide-surge (FEMA, 2016a), surge-riverine (FEMA, 2016c), and tropical storm (or hurricane) type flooding events (FEMA, 2016b). Currently, FEMA does not cover compound coastal flooding from high marine water levels and precipitation. However, this work suggests, at high return periods the sampling method is critical to characterizing both univariate and joint probabilities.

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Structural scenarios provide a quantitative context to frame flood vulnerability. In the structural failure context, AC sampling significantly underestimates flooding at all return periods, and AM sampling underestimates severe (i.e., 100-year) events, echoing previous AC and AM samplings issues. Similar values between most copulas support the suggestion that choosing a reasonable copula will provide robust results in these types of applications. Precipitation events in the Structural scenario ( flooding. This significant flooding at all return periods suggests severe flood vulnerability, which is validated by frequent closures of PCH. This structural function provides a quick and simple alternative to poorly performing bathtub flood models (e.g., Bernatchez et al., 2011;Gallien et al., 2011Gallien et al., , 2014Gallien, 2016) to quantitatively explore flood severity while accounting for infrastructure and joint probabilities. OWL pairs in high return periods often exceed the current data record's maximums (e.g. Table 8). This study is limited to the available data records and sea level rise clearly imparts a non-stationary trend. Current water level values restricted to today's distribution tails, will become more frequent in the next century (Taherkhani et al., 2020). For example, Wahl et al. (2015) suggests a previously 100-year event in New York is now a 42-year event based on the increasing correlation between extreme 370 precipitation and storm surge events. Similarly, our results suggest increasing precipitation and, particularly, OWL levels.

Conclusions
Univariate, conditional, and bivariate compound flood risk from OWL and/or precipitation were explored at three sites in a tidally dominated, semi-arid region. Seventeen copulas were considered. Previous studies typically relied upon a small number of copulas (e.g. Clayton, Frank, Gumbel, Student t, and Gaussian) for compound flooding assessments. In this case, the 375 Fischer-Kock, Roch-Alegre, and Tawn copulas produced similar, quality fits across all sampling methods. Although, in some cases, the Tawn produced conservative results. Independent and Cubic copulas consistently produced poor fits which under-/overestimated values and favored either precipitation or water level dominated events. Multiple copulas exhibit similar goodness of fit values (Fig. 4) and most probable pairs (e.g., Fig. 6, 7) suggesting a number of potential copulas may provide a robust multivariate analysis. This work focused solely on the exploring the ::::::: exploring : conditional and joint probabilities of OWL and 380 precipitation in a tidal and wave dominated semi-arid region. Although wave impacts were not included in this assessment, they are fundamental to coastal flooding, particular :::::::::: particularly in regions subjected to long period swell. Joint probability methods explicitly including wave contributions to compound flood risk characterization are needed.