A total of 275 observing stations were considered for this study, located across the study area that includes the coasts or coastal regions of New York City, Long Island, and Long Island Sound (Fig. 1). Three data types were used in this analysis: (1) daily precipitation totals, (2) daily coastal non-tidal residuals representing storm surge, and (3) observed monthly groundwater levels measured in the uppermost unconfined hydrogeologic unit near the coast. First, total calendar day (24 h) precipitation values were retrieved from 21 National Oceanic and Atmospheric Administration (NOAA) precipitation observing stations (NOAA NCEI, 2023) for a 52-year period spanning calendar years 1970 through 2021. On days when precipitation fell as snow, the liquid water equivalent was used as the precipitation value for that day as provided in the associated daily NOAA data report. Second, coastal water levels were retrieved from 12 NOAA water-level stations (NOAA CO-OPS, 2023) with recorded hourly water levels (m) and 22 U.S. Geological Survey (USGS) water-level stations (U.S. Geological Survey, 2023) with recorded 15 min water levels that have record lengths longer than 9.9 years between 1970 and 2021. A 33 h low pass filter was applied to the observed hourly water level time series to compute the non-tidal residual (NTR), which is conceptually akin to “storm surge” (Cook and Herdman, 2025). The computed NTRs were subsampled to daily maximum values. Third, monthly groundwater levels were retrieved using the USGS National Water Information System (NWIS; U.S. Geological Survey, 2023) for 220 unconfined observation wells throughout Long Island, New York City, and southern Connecticut for the calendar years 1975 through 2021. A starting year of 1975 for groundwater optimized the record completeness based on data availability. Table 1 contains all station identification numbers, locations, and map I.D.s linking station locations to the maps in Fig. 1a.

Some real-time groundwater monitoring networks are available on Long Island at daily temporal resolution (U.S. Geological Survey, 2023) and can be used to analyse the response of groundwater to compound coastal flooding. However, the monitoring frequency is monthly for many wells with longer periods of record in Long Island, New York City, and Southern Connecticut. Therefore, monthly groundwater observations were used in this study. The centroid locations of the groundwater wells selected for each station pair are shown in Fig. 1b; the well selection process is described in detail below.

Missing values for each of the three data types were filled using neighbouring, correlated stations at a daily timestep for precipitation and NTR, and at a monthly timestep for groundwater. The imputations were carried out using the ARCHI R package (Levy et al., 2024; R Core Team, 2024, version 4.4.1), which iteratively searches the available input data for multiple correlated reference stations and uses regression to predict missing values at the target station. Each of the three data types were imputed using the ridge regression option within ARCHI, except for the case where only one reference station was available, and in that case simple linear regression was used. A Pearson correlation coefficient of 0.6 and a Nash–Sutcliffe Efficiency (NSE) of 0.4 were used as the minimum threshold for accepted regression models in the ARCHI algorithm. Special consideration was given to the precipitation dataset because predictions from the ARCHI algorithm sometimes included near-zero negative values; predictions that were less than 1 mm were censored to zero. Full imputation statistics are shown in Supplement Tables S1, S2, and S3 and the proportion of imputed to observed records across the study area is summarized in Fig. 2. To further evaluate imputation quality, five percent of the observed values for each of the three data types were withheld (daily precipitation in millimeters, daily storm surge as NTR in meters, and monthly groundwater in feet below land surface), including separate consideration of wet day (observed prcp >1 mm) and dry day (observed prcp <1 mm) precipitation. The ARCHI algorithm then imputed those values and were compared to the observed values by root mean squared error (RMSE) and bias. It should be noted that imputed records may retain missing values where no correlated reference station had concurrent observations available, for example, during early portions of the record when monitoring network density was lower.

Using the complete imputed data records, 24 precipitation-coastal station pairs were selected based on proximity. Each pair was subsequently paired with groundwater observation wells to form a station triad, reflecting the three data streams contributing to each analysis location. Individual stations may contribute to more than one triad where geographic proximity warranted inclusion. Groundwater observation wells were selected using a cluster-based approach centered on the geographic midpoint between each precipitation/coastal station pair in decimal degrees. Beginning with a 5 km search radius around each midpoint, wells were selected based on the following criteria: (1) at least 90 % data availability from 1975 to 2021 in the imputed monthly time series, (2) 100 % data availability from 2010 to 2021 to capture recent extremes, and (3) at least one observation of depth to water less than 50 feet (15 m) below land surface (b.l.s.), to exclude deeper aquifer zones or wells not representative of near-surface conditions. If fewer than two qualifying wells were found within the 5 km radius, the radius was incrementally expanded until the criteria were met. Final search radii for each midpoint are listed in Table 1, with a maximum of 23 km at Triad 12. Up to 10 wells per search radius were retained based on proximity to the precipitation-coastal station midpoint. Final selections were manually reviewed to confirm hydrogeologic consistency within each cluster, specifically that selected wells were completed in the same unconfined hydrogeologic unit, exhibited seasonal water level patterns consistent with neighboring wells, and were representative of ambient conditions. Final station triad groups are listed in Table 1 and respective group centroids shown in Fig. 1b. A list of all the selected wells and their associated triads are listed in Table S4.

To evaluate the relations between daily precipitation and storm surge, event pairs were selected and modeled using copulas with a “two-sided sampling approach” (Jane et al., 2022). Data were prepared for bivariate modeling by detrending coastal NTR (storm surge) values over a three-month moving window. No trends were detected in the daily precipitation time series. High or extreme events were identified in each dataset using a peaks-over-threshold (POT) approach, applying thresholds from the 90th to the 99th empirical quantile at each station. To ensure the selection of independent events, a declustering separation window of 10 d for precipitation and 6 d for NTR was established, which aligns with the lag times for considering concurrent events: ±5 d for precipitation and ±3 d for surge (Agel et al., 2015; Barbot et al., 2024). Final POT thresholds were chosen to limit the number of independent events per year to between 3 and 6 while maximizing the Kendall tau correlation coefficient between the two variables.

To create two distinct biconditional datasets the R package Multihazard (Jane et al., 2020) was used with the Multihazard::Con_Sampling_2D_Lag function. For the precipitation-conditioned dataset (CoP), 24 h precipitation totals exceeding the selected threshold were identified as conditioning events, and the maximum NTR occurring within a ±5 d window of each precipitation event was extracted. For the surge-conditioned dataset (CoS), NTR values exceeding the selected threshold were identified as conditioning events, and the maximum precipitation occurring within a ±3 d window of each surge event was extracted. Time lags of ±5 d for CoP and ±3 d for CoS were based on findings that average coastal storm surge events around New York have durations ranging from 1.6 to 3.3 d (Barbot et al., 2024), and that the most common duration for extreme rain events in coastal areas of the Northeast is between 2 and 5 d (Agel et al., 2015). This approach accommodates potential mismatches between peak rainfall and storm surge that still have overlapping events, as well as delays in water reaching the coast via overland flow.

Biconditional precipitation-surge event sets were assessed for correlation using Kendall tau for each triad. Kendall tau is a rank-based nonparametric correlation coefficient that measures the strength of monotonic dependence between two variables, defined in Eq. (1) as: 1τ^=nc-nd12n(n-1) where nc and nd are the numbers of concordant and discordant pairs respectively and n is the sample size. Kendall tau was used here because it does not assume normality of the marginal distributions, is robust to extreme values, and has a direct mathematical relationship to copula dependence structure through its connection to the copula parameter (Genest and Favre, 2007).

To identify temporal changes in this correlation structure, 20-year moving windows were used to re-compute the Kendall tau for selected events inside that time window, then shifted by one year across the time range of the dataset. To evaluate temporal changes in dependence structure, the empirical upper tail dependence coefficient (λ^U hereafter referred to as uTDC) was computed separately for the first and second halves of the study period. The uTDC was estimated using Eq. (2): 2λ^U=1nu∑i=1nIUi>u,Vi>u where Ui and Vi are pseudo-observations on the unit interval, I is the indicator function, and nu is the number of observations exceeding the threshold u. Estimates were computed for u=0.6, representing the upper half of the distribution, and u=0.9, representing the upper tail. Calculations were performed for the periods 1975–1995 and 1996–2021 to assess changes in upper tail dependence over time and evaluate the need for a nonstationary framework. To further evaluate marginal stationarity, linear regression of POT exceedance magnitudes against time was performed for both precipitation and surge across all 24 triads under both conditioning approaches. Slopes and associated p-values are provided in Table S5.

To model the dependence structure in the data, each variable (precipitation and NTR) in the biconditional datasets was transformed into a uniform distribution by computing their rank-based pseudo-observations. The pseudo-observations are “plotting positions” using common nomenclature in hydrologic hazards (Asquith and others, 2017, Appendix 2), lie on [0,1], and correspond to the data mapped to rank-based cumulative probability space. An independence test of the pseudo-observation pairs was completed before selecting a copula model, where the null hypothesis is bivariate independence using the R function VineCopula::BiCopIndTest (Nagler et al., 2023; Genest and Favre, 2007). In the cases where the pseudo-observations are quantitively independent (p-value >0.05), then the independence copula was selected for those station pairs. For bivariate data pairs exhibiting statistically significant dependence, parametric copula models were fitted using maximum likelihood estimation. The candidate set included two elliptical copulas: Gaussian and t, and three Archimedean copulas: survival Clayton, Gumbel, and Frank. These six copulas were selected to capture a range of tail dependence structures relevant to the variables of interest (rainfall and NTR). Specifically, survival Clayton and Gumbel exhibit upper tail dependence, the t copula exhibits symmetric tail dependence (both upper and lower), and the Gaussian and Frank copulas are tail-independent. These copulas are relatively common tools for practitioners and are all permutation symmetric, which means for the copula C(u,v) that C(v,u)=C(u,v). Such symmetry is therefore an implicit assumption for this study.

The best fitting copula was selected using the minimum Akaike information criterion (AIC, Akaike, 1973; Asquith et al., 2017, Appendix 4). The AIC offers a comparative measure of fit for candidate copulas, identifying the model with the lowest AIC as the optimal choice. In instances where the difference in AIC between the top candidate and the next best model was less than 2 (Δ AIC <2), indicating a statistical tie in support, an additional screening was performed. Specifically, the empirical upper tail dependence coefficient (uTDC) of the observed data was compared against the distribution of uTDC values derived from 500 bootstrap simulations of each candidate model. If the absolute difference between the empirical uTDC and the median of the simulated uTDCs exceeded 0.1, the model was considered to provide a poor approximation of tail behavior and was excluded from consideration. The remaining model with the better agreement in uTDC was selected. The uTDC threshold of 0.1 represents a meaningful departure given that empirical uTDC values across all 24 triads ranged from approximately 0.10 to 0.25 at u=0.6. The median rather than the mean of the bootstrapped uTDC values was used as the reference because bootstrap distributions of uTDC can be skewed under weak dependence or small sample sizes, making the median a more robust measure of central tendency. An absolute difference threshold was preferred over a standard deviation based criterion because uTDC is bounded on [0,1], making absolute comparisons on the same scale more interpretable.

Graphical diagnostics and a goodness-of-fit hypothesis test were used to assess absolute fit and ensure that the selected model adequately represents the raw data. The quality of fit was graphically inspected by comparing the fitted parametric copula to the empirical copula by contour lines along cumulative probability values (the “level curves” in copula nomenclature, not shown). Additionally, a rank-based goodness-of-fit test was applied to further assess the fit of the selected copulas (Huang and Prokhorov, 2014). This test is semi-parametric, using a parametric copula and nonparametric, empirical marginals where the null hypothesis pertains to the assumption of the data following the specified copula model using the VineCopula::BiCopGofTest function in the VineCopula R package (Nagler et al., 2023).

When computing return periods for bivariate data using copulas, there is an infinite number of data pairs (precipitation-surge) associated with a single joint return period that can be graphically represented by contour lines instead of univariate singular estimates. All joint return periods computed in this study are AND-type, corresponding to the simultaneous exceedance of both precipitation and surge thresholds, as distinct from OR-type return periods where exceedance of either variable alone is sufficient. Return period contour lines associated with each biconditional dataset were computed using the fitted copula through Eq. (3) for the AND joint return period, examining the probability of a specific magnitude of precipitation and coincident surge: 3RPAND=μ1-u-v+C(u,v) where μ is the average interarrival time of events in years, and u and v are the marginal cumulative distribution functions (CDFs) associated with each variable, and C(u,v) is the joint CDF of the selected copula function. For a fixed return period T, Eq. (3) is satisfied by a continuous set of (u,v) combinations lying on [0,1]×[0,1], defining a contour line in bivariate probability space rather than a single point estimate. Under the assumption of independence, the joint AND return period is the product of the two marginal return periods, incorporating their respective exceedance probabilities. In contrast, under dependence, this relation is altered, and for positively correlated variables, the joint AND return period is shorter than under the independence assumption.

For each triad, and for the subset of univariate marginal return periods of 2, 10, 25, 50, and 100 years for both precipitation and surge, the ratio of the bivariate AND return period under independence to the dependence case was calculated for each combination of univariate return periods using the selected copula model. This ratio of return periods, or return period adjustment, represents the degree of dependence between the variables across each unique combination of univariate return periods (u and v), allowing the measure of dependence between the variables to be assessed in units of return period (Zscheischler and Seneviratne, 2017). To illustrate, consider a precipitation event with a univariate return period of 4 years and a coincident surge event with a univariate return period of 50 years. Under the assumption of independence the joint AND return period is the product of the two marginal return periods: 4×50=200 years. Under dependence, if the return period adjustment factor is 8, the joint AND return period is 200/8=25 years, meaning the compound event is 8 times more likely to occur than independence would predict.

To simplify the suite of return period adjustments across the unique u and v combinations, the array of return period adjustments was collapsed to a single value by weighted averaging. For each triad location, the paired events were randomly sampled 500 times with replacement, preserving pair structures and number of bivariate events. Copula parameters were re-estimated while maintaining the copula family type of the full dataset, and bivariate return periods and their corresponding adjustments from the independence case were re-computed. From the resulting distribution of return period adjustments corresponding to each unique pair of univariate marginal return periods, the 0.025 and 0.975 quantiles were extracted and used as 95 % confidence intervals around each return period adjustment. The width of the 95 % confidence interval is representative of bivariate sampling uncertainty around the return period adjustment calculations, and the inverses of these widths were used as weights in the final weighted averages of return period adjustments for the CoP and CoS paired values for each station triad. This results in two weighted average return period adjustments per station triad. The weight assigned to each return period adjustment was computed according to Eq. (4): 4wi=1CIi where CI_i is the width of the 95 % confidence interval for the return period adjustment at univariate return period combination i, derived from the 500 bootstrap samples. The weighted average return period adjustment for each triad was then computed according to Eq. (5): 5RP‾=Σiwi⋅RPiΣiwi where RP_i is the return period adjustment at each unique combination of univariate marginal return periods. This weighting scheme assigns greater weight to return period combinations where bootstrap uncertainty is smallest, which in practice corresponds to shorter univariate return periods where sample sizes are largest. The resulting return period adjustments and bootstrap uncertainty for each triad are presented in Sect. 4.4.

For each triad, median monthly groundwater levels were computed from the selected wells within each associated cluster. These monthly time series were linearly interpolated to daily resolution. Groundwater levels (in feet b.l.s.) were then extracted for the date of each event type: rainfall above threshold, surge above threshold, and concurrent rainfall/surge events. This extraction enabled assessment of groundwater conditions during different types of compound events. Because the groundwater levels may not have been measured during the actual storm event, the values used in this analysis may not represent the actual groundwater response to coastal and precipitation events.

To characterize groundwater-related hazard, the shallowest groundwater levels (minimum depth to water b.l.s.) during any compound event (both CoP and CoS) were used to assign a groundwater hazard score. Depths of 6 ft (1.8 m) or less were assigned a score of 2 (high hazard), depths between 6 ft and 15 ft (1.8 to 4.6 m) were scored as 1 (moderate hazard), and depths >15 ft (4.6 m) were scored as 0 (low hazard). These thresholds reflect physical infrastructure vulnerability criteria: depths less than 6 ft have the potential to interfere with drainage infrastructure and natural soil infiltration (Bosserelle et al., 2022), while depths between 6 and 15 ft are likely to intersect with basements and subsurface infrastructure (Conestoga-Rovers and Associates, 2007; New Jersey Department of Environmental Protection, 2021). These thresholds are consistent with those used in the companion groundwater emergence hazard analysis for the same study area (Masterson et al., 2025; Welk et al., 2025a), for direct comparison of hazard scores across the suite of regional hazard products.

The groundwater hazard score was combined with two scores based on the dependence structure between precipitation and surge. First, a triad received 1 point if either CoP or CoS event datasets exhibited upper tail dependence, as determined by fitting a copula with upper tail dependence. Second, a triad received 1 point if symmetrical dependence was observed, meaning a non-independent copula was selected for both CoP and CoS event types.

The three component scores (groundwater depth, upper tail dependence, and dependence symmetry) were summed and rescaled to yield a final compound hazard score ranging from 1 (lowest) to 5 (highest) for each triad.

To interpolate these results across the entire study area (the coasts of Long Island Sound and the south shore of Long Island), each groundwater centroid location was initially assigned to one of eight clusters using k-means clustering (MacQueen, 1967), implemented with the scikit-learn Python library (Pedregosa et al., 2011). Clustering was based on the following six features: (1) average return period shift conditioned on precipitation (CoP), (2) average return period shift conditioned on surge (CoS), (3) median minimum groundwater depth (in feet), (4) groundwater hazard score, (5) biconditional dependence score, and (6) upper tail dependence score. The number of clusters (k) was selected by evaluating silhouette scores over a range of candidate k values; the highest score occurred for k=8. Because k-means does not enforce geographic contiguity and some of the statistically derived clusters consisted of multiple disconnected spatial regions, a spatial post-processing step was applied to separate Connecticut and the North and South shore of Long Island. Non-contiguous cluster components were separated into distinct regions to ensure that each final cluster represented a coherent geographic unit. This procedure resulted in 9 final regions, each containing between one and four stations, while preserving the underlying k-means classification structure.

For each cluster, a centroid was calculated and used to generate Voronoi polygons (Aurenhammer, 1991) that partitioned the entire study area. Separate Voronoi tessellations were created for Connecticut (CT), and for the north and south shores of Long Island. Within each Voronoi polygon, 900 m grid cells were assigned the average compound hazard score of the stations in the corresponding cluster. Averaging was then masked and restricted to 900 m grid cells located within the coastal 100-year flood (0.01 annual exceedance probability) hazard extent for the study area, as defined by Welk et al. (2025b). This grid is the same grid used for rainfall hazard (Welk et al., 2025b), coastal flood hazard (Cook and Herdman, 2025), and groundwater hazard (Welk et al., 2025a) across the same study area, allowing for direct spatial comparison of hazard scores across variables. The spatially continuous hazard map is based on interpolation of results from discrete monitoring stations. These stations are assumed to be representative of broader conditions, but the map does not account for local variability in precipitation, coastal water levels, or groundwater depth at locations where no measurements were available. The analytical workflow for compound flood hazard assessment, from data imputation through spatial interpolation of hazard scores, is summarized in Fig. 3.

A total of 21, 34, and 207 observing stations were used to fill in missing records for precipitation, coastal NTR, and groundwater, respectively. Then, a subset of these stations, 13 precipitation, 15 coastal, and 58 groundwater observing stations, were used after imputation for input to the copula models and the final combined compound flood hazard score. The proportions of observed and imputed values are presented in Fig. 2 for these stations, separated by each year of record from 1970 through 2021. Precipitation data had more than 80 % observed values throughout the study period, whereas observed values for coastal NTR averaged about 15 % until 2008 and 80 % through 2021. Observed data comprised about 20 % of groundwater records for 1975–1990, after which the proportion of observed records increased to between 40 % to 60 %. Despite the high proportion of imputed values in the NTR and groundwater datasets, their strong intrinsic correlation and sufficient duration of overlap justified their inclusion. Precipitation data exhibited lower cross-correlation; however, at least 80 % of precipitation values were observed in any given year of the study period, exceeding the proportion of observed values in the NTR and groundwater datasets. Errors (RMSE and bias) were higher than for coastal water levels or groundwater, reflecting the greater spatial and temporal variability of precipitation (Tables S1–S3). However, because the precipitation record contained a high proportion of observed values, only a small fraction of the series was imputed, limiting the influence of these higher errors.

The accuracy of the regression imputation process was assessed using the results from the holdout analysis, comparing observed to imputed across precipitation, coastal NTR, and groundwater datasets (Table 2). Higher error and bias resulted from wet-day precipitation values, where imputation on wet days were on average 1.5 mm lower than observed values, and dry-day imputations were on average 0.34 mm higher than observed (zero) values (Table 2). Taken as a whole, holdouts from the entire precipitation dataset were on average 0.08 mm lower than observed values. Corresponding RMSEs for each precipitation holdout dataset were highest for wet days, lowest for dry days, and approximately 4.5 mm for all precipitation days as a whole. The NTR and groundwater datasets were slightly under-predicted by the imputations; however, these errors were relatively small (less than 1/100 of a meter and foot, respectively). Full imputation statistics for the entire dataset (not withheld values) are provided in Tables S1–S3.

Selected precipitation and surge threshold probabilities ranged from 0.97 to 0.99 across precipitation and surge datasets for all 24 triads (Table 3) and resulted in the average number events ranging from 3.1 to 5.8 events per year. Selected events conditioned on precipitation (CoP) showed a slightly seasonal pattern during the warmer months of the year, whereas events conditioned on surge (CoS) occurred distinctly between the months of October to April (Fig. 4). Sample size also varied across triads and sampling conditions, ranging from 162 (triad 23, CoP) to 308 precipitation-surge events (triad 22, CoP). Correlations across both datasets were weak, with higher and more substantial correlations when data were conditioned on surge. Mean Kendall tau of conditional datasets were 0.06 for CoP samples, and 0.13 for CoS samples. An example of data for Triad 15 (The Battery, NY) with selected precipitation and NTR thresholds is shown in Fig. 5.

Sampled events that were conditioned on surge showed more dependence than those conditioned on precipitation based on selected copula models. Of the triads exhibiting statistically significant dependence, upper tail dependence was present in 6 of 24 triads under CoP and 12 of 24 triads under CoS, as determined by selection of a copula family exhibiting upper tail dependence (Table 4). Independence was evident in 14 of the 24 triads where event selection was conditioned on precipitation, whereas only one of the triads (triad 10) was found to have independent data when events were conditioned on surge. For events conditioned on surge, 12 of 24 triads exhibited upper tail dependence (Table 4). Changes in Kendall tau for the period of study (1970–2021) were either slightly positive or slightly negative across all 24 triads but increased on average less than 0.1 over the study period (e.g., Triad 15, Fig. 6). Changes in the nonparametric upper tail dependence coefficient during the first half (1970–1995) to the second half (1996–2021) of the period evaluated in this study showed no persistently increasing or decreasing patterns across the 24 triads (Fig. 7). Regression of POT exceedance magnitudes against time revealed no regionally coherent trend in precipitation extremes across the 24 triads. Surge extremes showed slight decreasing trends at a subset of triads along the western south shore of Long Island and coastal Connecticut, with slopes ranging from -0.003 to -0.007 m yr⁻¹ (Table S5). The direction of these trends is conservative with respect to compound hazard assessment. Based on these results, stationarity was assumed for this analysis.

For samples for which independence could not be ruled out, the independence copula was assigned; this explicit “snap” to independence means that reliance on a given nonindependent copula model with its empirical parameter was not made for this study (Table 4). Graphical comparison to the empirical copula (not shown), and p-values from the semi-parametric goodness-of-fit (GOF) test indicate the copula chosen by the AIC and uTDC criteria acceptably fit with the empirical data (p-values for GOF test shown in Table 4). Model fit diagnostics for all candidate models are shown in Tables S6 and S7.

Figure 7 and Table 5 show and list, respectively, the results from the copula analysis as return period adjustments between the assumption of independence and dependence for concurrent precipitation-surge events. The weighted average return period adjustment encompasses all values across the selected univariate return period pairs, inversely weighted by the variability from the bootstrap resampling (Fig. 8a). Because higher return period adjustments generally indicate more variability between the bootstrapped samples, the weights put more emphasis on shorter univariate return period events. Figure 8b illustrates this for Triad 15, showing how the return period adjustment varies across univariate return period combinations for surge along with associated 95 % confidence intervals. The curvature of this relationship reflects the two-dimensional nature of the joint AND return period contour described in Eq. (2), where each point along the curve represents a different (u,v) combination satisfying the same joint exceedance probability. Weighted average adjustments ranged from 1 (independent data) to 8.51 (Triad 4, conditioned on surge, Table 5), meaning that coincident rain-surge events are more than eight times more likely to occur when taking their dependence structure into account (that is, the joint AND return period under dependence is approximately eight times shorter than under the assumption of independence, reflecting the observed historical dependence structure rather than any change in physical forcing). The average return period adjustment conditioned on precipitation was 2.99, whereas the average adjustment conditioned on surge was 4.32 across all station triads. The magnitude of period adjustments corresponds to the strength of upper tail dependence associated with the copula models as well as statistically significant correlations represented in the Kendall tau correlation coefficient (Tables 3 and 4).

Over the 1975–2021 period of data, the shallowest (minimum) depth to groundwater during pooled compound event dates was extracted for each station triad's well cluster and used to assign the groundwater hazard score (Table 5). Groundwater shallower than 6 feet or 1.8 m was associated with triads 17 and 23 along the southern shore of Long Island and Connecticut, respectively. Depths to water between 6 and 10 feet (1.8 to 3 m) were found around the coastline of Long Island Sound at triads 11, 13, 14, 16,and 24. The spatial distribution of the event-based groundwater levels are shown in panel C of Fig. 10. Minimum groundwater depths less than 6 feet (1.8 m) have the potential to interfere with drainage infrastructure, natural infiltration of soils, and may contribute to more overland runoff during precipitation events (Bosserelle et al., 2022). Groundwater levels between 6 and 15 feet (1.8 to 4.5 m) will likely intersect with basements and other subsurface infrastructure (Conestoga-Rovers and Associates, 2007; New Jersey Department of Environmental Protection, 2021). During most precipitation-surge events, groundwater across the study area was elevated (more shallow) above median levels (Fig. 9). Because of the seasonal pattern of high storm surge, events that were sampled conditioned on surge occurred during the winter when regional groundwater storage and levels are highest (Bjerklie et al., 2012; Li et al., 2015).

Overall compound flood hazard rating was scored according to the criteria described in Sect. 3.4, stratifying the scoring by magnitude of precipitation-surge return period adjustments and shallow (0 to 6 feet or 0 to 1.8 m) versus deeper (6 to 15 feet or 1.8 to 4.6 m) monthly average groundwater levels). Final scores ranged from 1 to 5 and are generally higher (indicating more frequent co-occurrence of high rainfall, surge, and shallow groundwater) on the western south shore of Long Island, as well as along the Connecticut coast. Final compound hazard scores along with their scoring components are shown spatially in Fig. 11, plotted at the centroid of groundwater wells associated with each precipitation–coastal station pair. Interpolated results across the study area are shown in Fig. 11a and as a shapefile in Glas et al. (2025). Compound flood hazard scores were lowest across central and eastern Long Island, both south and north shores. The compound hazard scores, supporting univariate hazard layers, and 900 m gridding geometry are available for interactive exploration at the station-triad and 900 m grid scale via an online mapping application (Finkelstein et al., 2025, https://ny.water.usgs.gov/maps/compoundflooding/, last access: 10 April 2026). The individual ordinal components contributing to the composite hazard score shown in Fig. 11a are presented in Fig. 11b–d: biconditional dependence (Fig. 11b), upper tail dependence (Fig. 11c), and shallow groundwater depth (Fig. 11d).

Record imputation introduces uncertainty into these results, as the quality of gap-filled data directly influences threshold selection, dependence estimation, and groundwater percentile calculations. Extreme values that have been estimated by imputation may be under-represented because of the tendency for regression to underpredict the variance of time series (Newman, 2014), potentially underestimating the true variability and frequency of compound flooding. Imputation techniques that include a maintenance of variance (Vogel and Stedinger, 1985) may yield results that more accurately represent the variance of the system; however, these methods generally have lower predictive power than ordinary least squares or ridge regression (Levy et al., 2025) and should be used with caution if records show autocorrelation patterns typical of coastal water levels and groundwater (Matalas and Jacobs, 1964). To the extent that imputation dampens extreme values, tail dependence estimates and return period adjustments derived from imputed portions of the record may be slightly conservative, representing a lower bound on compound hazard at locations where early NTR and groundwater records relied heavily on imputed values. Formal propagation of imputation uncertainty through the copula framework remains a direction for future work. Data imputation for this study is deemed prudent because imputation gains access to multiple stations throughout the study area that do not have complete data and have been traditionally left out of previous studies of compound flooding in the region (Ghanbari et al., 2021; Lai et al., 2021; Nasr et al., 2023; Wahl et al., 2015). Threshold selection approaches widely vary across the literature and can introduce variability in the results by influencing sample sizes and consequently the robustness of derived conclusions. Uncertainty associated with different threshold detection and declustering methods can be further increased under potentially nonstationary conditions (Agilan et al., 2021). Employing a variety of threshold selection techniques and investigating the sensitivity of results may be necessary to fully understand the spatial distribution of extreme events. The threshold selection procedure used here, which maximizes Kendall tau within the constraint of 3–6 events per year, may introduce a slight bias toward stronger dependence estimates relative to fixed-threshold approaches. However, the 3–6 events per year constraint limits the range of thresholds available for optimization and therefore the magnitude of any such bias.

Multiple copula models were studied to understand precipitation-surge dependence better, limiting those models to two choices of elliptical copulas and four Archimedean types that may display tail dependence and such tail dependence in the appropriate tail (for this study the upper tail). These choices were based on previous studies (e.g., Phillips et al., 2022) and associated fit metrics for each copula choice. However, some studies have used a single copula model to describe a region so that the differences in dependence arise from the variability of parameter estimates instead of the practitioner's choice of copula model (e.g., Chen et al., 2025). This study incorporates elements of sampling and parameter uncertainty in the bootstrap procedure but does not address imputation uncertainty or model selection uncertainty.

All candidate copula families used in this study are permutation symmetric, meaning C(u,v)=C(v,u), which assumes that the dependence structure is the same regardless of which variable is conditioned upon. Asymmetric copulas, which allow for directional dependence between precipitation and surge, were not considered. If the true dependence structure is asymmetric, the symmetric copulas used here may misrepresent the joint distribution in ways that could affect return period estimates at individual triads. The biconditional sampling approach used in this study, which produces separate CoP and CoS datasets, partially addresses this by allowing dependence to be assessed from both conditioning directions, and differences in results between CoP and CoS provide an indirect indication of potential asymmetry in the data.

Linear regression of POT exceedance magnitudes against time revealed small trends at a subset of triads, with surge extremes showing slight decreasing trends at stations along the western south shore of Long Island and coastal Connecticut (slopes ranging from -0.003 to -0.007 m yr⁻¹), and no regionally coherent increasing trend in precipitation extremes. These marginal trends are insufficient to justify a nonstationary framework, consistent with the split-period uTDC analysis in Fig. 7 and the guidance of Serinaldi and Kilsby (2015). Ultimately, we chose not to implement a nonstationary copula model because changes in tail dependence and overall correlation were judged as not substantial enough over the period of study to merit the introduction of additional uncertainty (Serinaldi and Kilsby, 2015).