Application of Bayesian Networks to hindcast barrierisland morphodynamics

Kathleen E. Wilson a,b,⁎, Peter N. Adams a, Cheryl J. Hapke c, Erika E. Lentz d, Owen Brenner c

a University of Florida, Department of Geological Sciences, Gainesville, FL 32611, United Statesb Cherokee Nation Technology Solutions contracted to U.S. Geological Survey, United Statesc U.S. Geological Survey, 600 4th St South, St. Petersburg, FL 33701, United Statesd U.S. Geological Survey, 384 Woods Hole Road, Woods Hole, MA 02543, United States

a b s t r a c ta r t i c l e i n f o

Article history:Received 16 September 2014Received in revised form 22 April 2015Accepted 23 April 2015Available online xxxx

Keywords:Coastal vulnerabilityMorphologic change predictionProbabilistic modelsFire Island, NY

Prediction of coastal vulnerability is of increasing concern to policy makers, coastal managers and other stake-holders. Coastal regions and barrier islands along the Atlantic and Gulf coasts are subject to frequent, largestorms, whose waves and storm surge can dramatically alter beach morphology, threaten infrastructure, andimpact local economies. Given that precise forecasts of regional hazards are challenging, because of the complexinteractions between processes on many scales, a range of probable geomorphic change in response to stormconditions is often more helpful than deterministic predictions. Site-specific probabilistic models of coastalchange are reliable because they are formulated with observations so that local factors, of potentially high influ-ence, are inherent in the model. The development and use of predictive tools such as Bayesian Networks inresponse to future storms has the potential to better inform management decisions and hazard preparation incoastal communities. We present several Bayesian Networks designed to hindcast distinct morphologic changesattributable to the Nor'Ida stormof 2009, at Fire Island, NewYork. Model predictions are informedwith historicalsystem behavior, initial morphologic conditions, and a parameterized treatment of wave climate.We refine a preliminary Bayesian Network by 1) increasing model experience through additional observations,2) including anthropogenic modification history, and 3) replacing parameterized wave impact values with max-imum run-up elevation. Further, we develop and train a pair of generalized models with an additional datasetencompassing a different storm event, which expands the observations beyond our hindcast objective. We com-pare the skill of the generalized models against the Nor'Ida specific model formulation, balancing the reducedskill with an expectation of increased transferability. Results of Nor'Ida hindcasts ranged in skill from 0.37 to0.51 and accuracy of 65.0 to 81.9%.

© 2015 Elsevier B.V. All rights reserved.

1. Introduction

Accurate prediction of coastal change is important for decisionmakers in barrier island coastal communities because of the high levelof vulnerability that low-lying coastal settings exhibit to storms thatdrive shoreline retreat, overwash, and dune erosion (H. John Heinz IIICenter for Science, Economics, and the Environment, 2000; Houser,2013; Nebel et al., 2013; Plant et al., 2010). Although debated, there isevidence that ocean storms may increase in frequency and intensity asa result of global climate change (Aumann et al., 2008; Bender et al.,2010; Church et al., 2013; Elsner et al., 2008; Emanuel, 2005; Komarand Allan, 2008; Melillo et al., 2014; Yates and Le Cozannet, 2012). To

prepare for a future with increased likelihood of coastal hazards, itis necessary to identify locations of high vulnerability (U.S. GeologicalSurvey National Assessment of Shoreline Change Project, http://coastal.er.usgs.gov/shoreline-change/, 2014b) and improve existingprobabilistic methods that forecast coastal change (Hapke and Plant,2010; Harley and Ciavola, 2013; Lentz and Hapke, 2011a).

Probabilistic models, including Bayesian Networks (BNs), are a use-ful predictive method in coastal systems because they are derived fromsite-specific observational data that integrate the dominant processesand controls on system behavior (Grezio et al., 2010; Loureiro et al.,2013). BNs are a quantitative tool, able to evaluate conditional prob-abilities between variables but are also valuable as conceptual models,visually representing independent and dependent variables in cau-sation relationships (Chen and Pollino, 2012; Palmsten et al., 2014;Stewart-Koster et al., 2010). This makes BNs particularly transferableto coastal management application because the framework andprobability forecast can be easily interpreted by policy makers andstakeholders.

Coastal Engineering 102 (2015) 30–43

⁎ Corresponding author at: U.S. Geological Survey, 600 4th St South, St. Petersburg, FL33701, United States. Tel.: +727 502 8099.

E-mail addresses: kwilson@usgs.gov (K.E. Wilson), adamsp@ufl.edu (P.N. Adams),chapke@usgs.gov (C.J. Hapke), elentz@usgs.gov (E.E. Lentz), obrenner@usgs.gov(O. Brenner).

http://dx.doi.org/10.1016/j.coastaleng.2015.04.0060378-3839/© 2015 Elsevier B.V. All rights reserved.

Contents lists available at ScienceDirect

Coastal Engineering

j ourna l homepage: www.e lsev ie r .com/ locate /coasta leng

The relationships between variables comprising BNs can be estab-lished by user knowledge, empirical evidence, or machine learning(Fienen et al., 2013; Palmsten et al., 2014). In coastal systems, an under-standing of physical controls such as wave climate, underlying geology,and anthropogenic activity helps to determine the variables and causa-tion structure of a BN. Probabilistic models have been used successfullyto predict coastal change (Grezio et al., 2010; Hapke and Plant, 2010;Lentz and Hapke, 2011a) as well as vulnerability to sea level rise(Gutierrez et al., 2011; Yates and Le Cozannet, 2012) and storms(Palmsten et al., 2014; Plant and Stockdon, 2012) at multiple sitesaround the world.

Recent work by Lentz and Hapke (2011a), Plant and Stockdon(2012), and Palmsten et al. (2014) designed BNs to predict barrierisland morphologic change in response to storms. Lentz and Hapke(2011a) presented two BNs to predict storm impacts on shoreline posi-tion and beach volume at Fire Island, New York (Fig. 1). The BNs weredeveloped with long term rates of shoreline change, initial conditions,and offshore wave observations. The original model structures and var-iableswere chosen based on anunderstanding of prominent controls onlong and short term system behavior at Fire Island. Model efficacy wastested for the Patriot's Day storm of 2007 and Nor'Ida storm of 2009,with ability to hindcast observed geomorphic change ranging from70% to 82%. Althoughmodel successwashigh, BN structure lacked a var-iable to represent anthropogenic activity and the training and validationdatasets were limited to two, 4-km study sites on the 50-km island.

Plant and Stockdon (2012) published models to hindcast shorelineand dune position, as well as dune crest change on Santa Rosa Island,Florida due to Hurricane Ivan. Theirmodels were a quantitative applica-tion of the Sallenger (2000) conceptual model of storm impact. Subse-quent work by Palmsten et al. (2014) sought to test the transferabilityof the Plant and Stockdon (2012) model to a new setting on the GoldCoast, Australia. Hindcasts by both sets of authors successfully explained60–72% of the observed variance in change of dune morphology orshoreline position, although neither Palmsten et al. (2014) nor Plantand Stockdon (2012) attempt to predict volumetric change.

The scale of storm impact is of great concern in coastal hazardassessment on barrier islands. The models presented by Plant andStockdon (2012) and Palmsten et al. (2014) were developed to predictthe damage to dunes from catastrophic storms like tropical cyclones. Inlocations with higher dune crest elevation or during storms with lowertotal water level, the two highest storm regimes, inundation and

overwash, (Sallenger, 2000) are rarely reached, therefore impact is lim-ited to the beach and lower portion of the dune. Nevertheless, thesestorms, particularly lengthy nor'easters, can cause sufficient erosion tothe beach to often prompt coastal managers to invest in costly nourish-ment or dune stabilization projects.

In this study, we sought to contribute to the existing body of knowl-edge by predicting beach morphodynamics under more moderatestorm conditions. To do so, we progress the work of Lentz and Hapke(2011a) by expanding the area included in our study, increasing thenumber of training cases, and introducing changes to the model struc-ture. Further, the work presented here differs from existing coastalchange BNs (Palmsten et al., 2014; Plant and Stockdon, 2012) by includ-ing unique model parameters and encompassing a longer time scaleover which the model is being tested. We examine the range of modelpredictive ability across five models, designed to hindcast net shorelinemovement (NSM) and beach volume change (BVC). BNs were devel-oped and trained with observations from the full length of Fire Island,an addition of 770 calibration locations over prior models (Lentz andHapke, 2011a). Beach nourishment data were incorporated into themodel to characterize humanmodification to the barrier island system.Few probabilistic modeling efforts have incorporated nourishment orcoastal infrastructure into the model framework; inclusion of develop-ment and anthropogenic activity is a progressive step for coastal man-agement toward utilizing the decision making applications of BNs(Chen and Pollino, 2012; Palmsten et al., 2014; Stewart-Koster et al.,2010). We replace wave impact hours, a comparison value of beachmorphology and parameterized run-up, (Hapke and Plant, 2010; Lentzand Hapke, 2011a; Ruggiero et al., 2001) with the maximum run-upelevation (Stockdon et al., 2006). Finally, we developed a generalizedset of models (NSM-G, BVC-G) which were trained with two datasetsfrom 2005 and 2009. Fig. 2 shows the identification of model type bythe morphologic change predicted (NSM or BVC), wave parameter(1:2), and model structure (N or G). We provide a detailed descriptionof the sensitivity analysis used to determine model structure inSection 3 and the results of the most successful model iterations arepresented in Section 4.

1.1. Bayes rule

Bayesian Networks are commonly used as statistical inference toolsin many disciplines including artificial intelligence, biochemistry and

Fig. 1. Location map of Fire Island, New York.

31K.E. Wilson et al. / Coastal Engineering 102 (2015) 30–43

ecology (Guisan and Zimmermann, 2000; Larranaga and Moral, 2011;Palmer and Ralsanen, 2002; Patenaude et al., 2011). In the geosciences,probabilistic models have been used in seismology (Lancieri and Zollo,2008; Sparks, 2003), volcanology (Jaquet et al., 2006; Marzocchi et al.,2004), tsunami forecasting (Geist and Parsons, 2006; Grezio et al.,2010) and in coastal systems (Fienen et al., 2013; Gutierrez et al.,2011; Hapke and Plant, 2010; Lentz and Hapke, 2011a; Palmstenet al., 2014; Plant and Stockdon, 2012; Yates and Le Cozannet, 2012).Probabilistic models can be advantageous over deterministic methodswhen complex system interactions exist but are difficult to quantify(Chen and Pollino, 2012; Palmsten et al., 2014). This advantage isbased on the ability of BNs to use inductive reasoning and causalrelationships to calculate joint probabilities between input variables.Further, probabilistic models are able to account for randomness inthe system and uncertainty in data collection (Grezio et al., 2010;Haneberg, 2000; Ruggiero et al., 2006; Thompson and Frazier, 2014).Finally, the ability to efficiently update themodel and adapt to changingconditions is especially valuable in modeling dynamic features such ascoastal morphology (Grezio et al., 2010).

Bayesian Networks are based upon Bayes' Theorem and its funda-mental equation:

p FijOj! "

¼ p OjjFi! "

" p Fið Þ=p Oj! "

: ð1Þ

Bayes' Theorem relates the probability (p) of a forecasted event (Fi)and the likelihood of the observations (Oj). The equation solves forthe posterior conditional probability of the forecast, Fi, given a set ofobservations, Oj. The numerator on the right contains the probabilityof the observations, given the forecast, p(Oj|Fi), and prior probabilityof that forecast, p(Fi). The denominator on the right is a normalizationfactor of the probability of the observations, p(Oj) (Grezio et al., 2010;Gutierrez et al., 2011; Plant and Holland, 2011; Plant and Stockdon,2012).

Causal relationships are fundamental to the probability functions ofBNs. The causation links between parameters are established by thenetwork user to best represent the modeled system. Similar to thenode links, bin boundaries are user-defined to discretize continuousdata. A thorough explanation of bin considerations is outlined in Plantand Holland (2011); however, a fundamental objective of binning is tostructure the bin boundaries wide enough to account for uncertaintyin the data, while balancing the number of observations per bin(Loureiro et al., 2013). The uncertainty of the data should not be largerthan the spacing of bin boundaries such that bins have higher resolutionthan the data training the model. It is also important to space the mar-gins so that all bins include a sufficient number of data points, otherwisethere may be inadequate constraint on parameter joint probabilities inmodel training.

2. Study site

Fire Island is a 50-km long barrier island on the southern shore ofLong Island and the Great South Bay, in Suffolk County, New York,USA. Our study area extends 46.7-km, from the eastern end of FireIsland at Moriches Inlet to the eastern boundary of Robert Moses StatePark (Fig. 1). The island is centrally located in the chain of barrier islandsthat span from Shinnecock Inlet in the east toward Rockaway Peninsula.The region has been well-studied in terms of its geologic framework,morphologic evolution, and sedimentology (Hapke et al., 2010; Hapkeet al., 2013a; Kana, 1995; Kana et al., 2011; Kratzmann and Hapke,2012; Leatherman, 1985; Lentz and Hapke, 2011b; Lentz et al., 2013;Nordstrom and McCluskey, 1985; Psuty and Silveira, 2009; Schwabet al., 2000; Schwab et al., 2013; Tanksi, 2007). The past studies provideinformation on the underlying geology, wave climate, and history ofmorphologic change, from which a BN model of large-scale coastal be-havior can be generated. Additionally, temporally dense survey datasetsof shoreline and dune toe position are available and reveal decadal scalemorphologic response across a range of stormy and quiescent waveconditions (Lentz et al., 2013).

The island is considered to be wave-dominated with a micro-tidal,semi-diurnal tidal pattern (Davis and Hayes, 1984). The mean tidalrange at the most proximal tidal stations, Montauk, New York, andSandy Hook, New Jersey are 0.6-m and 1.4-m, respectively. Wave datacollected from 1994 to 2012 at National Oceanic and AtmosphericAdministration (NOAA) National Data Buoy Center (NDBC) station#44025have amean significantwaveheight of 1.3-m,with ameandom-inant wave period of 7.3-s. Previous work has concluded that irregularbathymetry at Fire Island is linked with higher wave heights and energyin the east and a more dissipative environment in the west (Batton,2003; Hapke et al., 2010; Schwab et al., 2000; Schwab et al., 2013).

Kratzmann and Hapke (2012) classified Fire Island as a moderatelydeveloped barrier island, based on the presence of seventeen communi-ties that are interspersed within Fire Island National Seashore. Thecommunities are limited to private homes and businesses and do notcontain substantial infrastructure to be considered highly developed(Nordstrom, 2004). The island comprises a variety of land use types,including inhabited communities where modification (artificial duneconstruction/scraping and nourishment) occurs on beaches, inhabitedcommunities with beaches that are not modified, and areas of uninhab-ited, protected national seashore (Kratzmann and Hapke, 2012).

2.1. Anthropogenic modification

Soft stabilization techniques and hardened structures are a commonpractice used to reinforce protective and recreational beaches on Atlan-tic coast barrier islands (Kelley, 2013; Leonard et al., 1990; Nordstrom,2004; Psuty and Silveira, 2009). Two forms of soft-engineering, beach

Fig. 2. Schematic of the model naming convention. Net shoreline movement and volume change response variables are illustrated by the polygons at the top. Wave parameter types arerepresented by the squares: wave impact hours (white) or maximum run-up (gray). The data used to train the model is depicted with Nor'Ida (N), only the 2009 dataset, or generalized(G), both 2005 and 2009 data.

32 K.E. Wilson et al. / Coastal Engineering 102 (2015) 30–43

nourishment and scraping, are permitted by the National Park Serviceon Fire Island beaches (Kratzmann and Hapke, 2012; Lentz and Hapke,2011b; Lentz et al., 2013). At Fire Island, previous work has shownthat anthropogenic modification alters features in the immediate areaand influences down coast geomorphic change by altering sedimentavailability (Kratzmann and Hapke, 2012). Further, altering morphologyof the beach profile affects wave energy dissipation, making it more re-flective or dissipative. Lentz et al. (2013) determined that wider beachesat Fire Island have a history of being more dissipative, making them lessvulnerable to storm wave conditions (Kratzmann and Hapke, 2012;Lentz et al., 2013).

Stabilization projects involving hardened infrastructure are nolonger authorized on the island, although, two groins near Ocean Beach,which were constructed before the designation as a National Seashore,remain in place.

Beachnourishment involves obtaining sand froman inlandor offshorelocation and emplacing it on the beach face (Bruun, 1983; Leonard et al.,1990). Nourishment can initially produce over-steepened beaches dueto deposition on the upper beach but eventually results in wider, gentlysloping beaches (Nordstrom, 1994). Available records (CP&E, 2009;Gravens et al., 1999) indicate nourishment has occurred on Fire Islandfor nearly a century but has been employed most frequently in westerncommunities in recent decades.

Beach scraping involves moving sand from the lower beach or bermto the dune system. Scraping does not introduce new material intothe system but restructures the beach profile, often resulting in ahigher, more seaward dune crest, with a narrower beach (Kelley, 2013;Kratzmann and Hapke, 2012). Initial model formulations includedbeach scraping as a complementary variable to nourishment. However,analysis demonstrated that the model was insensitive to the scrapingnode and the model improved when scraping was removed. Studies

(Kratzmann and Hapke, 2012; Magliocca et al., 2011; Nordstrom, 2004;Wells and McNinch, 1991) have shown there are physical implicationsof beach scraping but model insensitivity to the data indicates thatthese effects are not recognized statistically by our BNs.

2.2. High wave events

The two study periods, April to November 2005 and July to Decem-ber 2009, were selected due to the availability of full island topographiclight detection and ranging (lidar) datasets within a single year. Lidaris a remote sensing technique which can be used to generate three-dimensional topographic surfaces (Zhang et al, 2005) from whichbeach and dune profiles are extracted. Changes in the beach profilesover the study period reflect the storminess and consequent morpho-logic impacts of a season, including several high wave events (Fig. 3).The most notable event of the 2009 observation interval (Fig. 3B1)is Nor'Ida, an extratropical storm that formed in November when rem-nants of dissipating Hurricane Ida intersected a northern high pressuresystem (Lentz and Hapke, 2011a). Hurricane Ida and the ensuingextratropical storm caused heavy rain, high winds, and extensive dam-age to coastal areas fromNorth Carolina throughNewYork. The lengthyduration (~3.5 days) resulted in high storm surge and flooding over thecourse of several tidal cycles (NOAA, 2012; U.S. Geological Survey,2014a). At Fire Island, Nor'Ida produced highwaves offshore and result-ed in overwash and sediment loss from the beach face (U.S. GeologicalSurvey, 2014a). The 2005 survey period was selected due to the inclu-sion of an unnamed, but notable nor'easter. The storm occurred inmid-October 2005 and had similar characteristics to Nor'Ida includingduration (Fig. 3A1; 1), maximum water levels (Fig. 4C), and observedgeomorphic change (Fig. 4H; I).

Fig. 3.Wave height and period time series from NDBC station 44025 andWaveWatch III hindcasts for the 2005 (A1–A2) and 2009 (B1–B2) survey periods. The wave height maxima inmid-October 2005 (A1) and mid-November 2009 (B1) identify the timing of the unnamed nor'easter and Nor'Ida, respectively.

33K.E. Wilson et al. / Coastal Engineering 102 (2015) 30–43

3. Methods

The net shoreline movement (NSM) and beach volume change(BVC) models build on the frameworks established by Lentz andHapke (2011a). The networks developed in this studywere constructedusing the software program Netica and were trained using thecounting-learning algorithm (Norsys, 2010). We present the results ofBVC-N2, the model which most closely reproduces the work of Lentzand Hapke by incorporating wave impact hours (2011a). The BVC-N2model structure differs slightly from Lentz and Hapke (2011a) basedon the inclusion of the nourishment index (NI) and initial volume. Accu-racy and a sensitivity analysis suggested that expandedmodel structurecould still be improved; therefore the remaining models (NSM-N, BVC-N1, NSM-G, and BVC-G) were created by restructuring the parameter

links (Fig. 5A; B) and varying the wave forcing (Fig. 2). Fig. 5 illustratesthe differences between the model structures for BVC-N2 (A) and theremaining models (B). The causation links between maximum run-upand the remaining parameters were removed in the later model formu-lations (B) because the initial conditions and the long term change ratesare dependent onwave conditions prior to, but not including, the surveyperiod.

A set of generalized models (NSM-G, BVC-G) were created to ex-pand model training beyond the prediction objective, Nor'Ida, andwere trained with both 2005 and 2009 datasets. Increasing networktraining data to two survey periods curtails overfitting themodel to asingular set of conditions, provides more scenarios from which themodel can learn, and is a step toward broader applications of stormresponse BNs.

Fig. 4. Illustration of alongshore variability in wave parameters (B–C) and observational data (A, D–G) to inform the shoreline movement (H) and beach volume models (I); 2005 data(gray); and 2009 data (black).

34 K.E. Wilson et al. / Coastal Engineering 102 (2015) 30–43

3.1. Establishment of model parameters

To establish the observational dataset, a shore parallel offshore base-line was generated from which perpendicular lines were cast as shore-normal transects. The study area is represented by 934 transects, spacedalongshore at 50-m intervals. The transects extend from the offshorebaseline to the landward side of the primary dune, capturing the geo-morphic features required for our BNs, such as shoreline and dune toeposition. Model parameters are evaluated at transect locations to revealgeospatial correlations and link our model results with known systembehavior. The training cases from 2005 and 2009 were complete along-shore datasets, without anymissing locations. The conditional probabil-ity distributions for the long-term change rates, initial conditions,nourishment index, wave parameter, and morphologic change are

shown in Fig. 6. The probabilities for each parameter vary betweenmodel type (A:E), given differences in discretization of the bins andthe data used to train the model. The highly skewed distribution inbin 1 of wave impact hours is apparent in E.

3.1.1. Wave parameterizationOurmodels are trainedwith oneof twohydrodynamic variables. The

original, and least successful model, BVC-N2, utilized a parameterizedwave forcing termed wave impacts hours (WIH) (Lentz and Hapke,2011a; Ruggiero et al., 2001), while the remaining models includemaximum run-up elevation (R2). WIH are the total number of hoursduring which the total water level (η98) exceeds the maximum eleva-tion of the beach. WIH is convenient because it is easily calculatedover a lengthy study period and represents the summed impact to the

Fig. 5.Conceptual representation of the twomodel structures. A.Model structurewhichmost closely resembles Lentz andHapke (2011a) by incorporatingwave impact hours but has beenexpanded to include nourishment and initial volume. B. The updated model structure used in NSM-G, NSM-N, BVC-G, and BVC-N1. Structural differences between the forms includeremoving all causation links from the wave parameter except to the morphologic change variable and adding a causation link from beach width to initial volume in B.

Fig. 6. Conditional probability distributions of the input variables in the BNs. The wave parameter in BVC-N2, wave impact hours, has a highly skewed probability distribution where allother variables, includingmaximumrun-up, havenormal to uniformdistributions across the bins. The y-axes inA throughD are consistent but the scale increases in E to accommodate thehigh likelihood of wave impact hours in bin 1. The x-axes are labeledwith the discretized binmidpoint value in each parameter; the values for the bin boundaries are shown in Tables 1Aand 1B. The causation relationships for the variables in the models are shown in Fig. 5.

35K.E. Wilson et al. / Coastal Engineering 102 (2015) 30–43

beach. Alternatively, R2 is difficult to incorporate over the full studyperiod, due to increased complexity of model training when a temporaldimension is included in the data, but has statistical advantages in aBayesian framework which we describe in Section 5.1.2.

WIH values are derived from wave and tidal data, beach slope andmaximum elevation at each transect. These data are used to calculatewave run-up, defined as the sum of set-up and swash, using:

R2 ¼ 1:1 0:35βffiffiffiffiffiffiffiffiffiffiffiHoLo

p$ %þ 0:75

2

ffiffiffiffiffiffiffiffiffiffiffiHoLo

pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiβ

0:08

2

þ 1

s

; ð2Þ

as developed by Stockdon et al. (2006), where β is beach slope, Ho issignificant wave height, and Lo is wavelength, related to wave period,T, by:

Lo ¼gT2

2π: ð3Þ

Waveheight andperiodwere obtained fromWaveWatch III hindcasts(Tolman, 2014; National Oceanographic and Atmospheric Administrationand Environmental Modeling Center, ftp://polar.ncep.noaa.gov/pub/history/waves, 2015) and verified against NDBC station #44025 data(Fig. 3) at the buoy location (40.251 N, 73.164 W). Wave conditions atthe 20-m isobathwere then extracted from theWaveWatch III hindcaststo calculate R2. Beach slope (β)was calculated using pre-storm conditionsat each cross-shore profile, assuming a constant slope from themeanhighwater (MHW) shoreline to dune toe. R2 is added to themeasured tide, ob-tained from the Montauk, New York tidal gauge (NOAA Tidal station#8510560), to determine η98 at hourly intervals. Each hourly η98 is thencompared to the maximum elevation between shoreline and dune toe,extracted from initial survey conditions. Hourly observations at whichη98 exceeds the maximum beach elevation are summed over the studyperiod to obtain the total number of WIH (Fig. 4B).

Maximum R2 (Fig. 4C) was extracted from the R2 previously calcu-lated forWIH. The known dates of the 2005 and 2009 stormswere que-ried for the maximum R2 at alongshore locations during the course ofthe storm. Therefore, the maximum R2 values do not necessarily repre-sent a single hourly observation but the transect-specific peak run-upthroughout the storm.

3.1.2. Historical and initial survey beach conditionsDigital Shoreline Analysis System (DSAS) (Danforth et al., 1992;

Thieler et al., 2009) was used to calculate initial beach width, definedas the distance between the dune toe and MHW shoreline, using April2005 and July 2009 morphology (Fig. 4D). Similarly, initial beach vol-ume (Fig. 4E) was calculated for both surveys using the integrationmethod developed by Kratzmann and Hapke (2012). Dune toe featureswere manually identified and extracted, guided by dune slope andelevation from topographic data. Dune toes are located seaward of theprimary dune and are identified primarily by the change in slope fromdune (10–30°) to berm top (0–10°) given an approximate elevationrange (2.7–4.3-m NAVD88). Shorelines from 2005 and 2009 were ex-tracted from topographic data at the 0.46-m (NAVD88) contour. Bins

for the beach width and initial volume parameters (Tables 1A; 1B)were broadly spaced to account for the positional uncertainty of theshoreline and dune toe which propagates through the beach widthand initial volume calculations. Beach width and initial volume vari-ables represent the pre-existing beach condition in the BNs.

DSASwas also used to calculate shoreline and dune toe linear regres-sion rates (LRR) (Fig. 4F; G) and netmovement of the shoreline position(Fig. 4H). Shoreline and dune toe surveys were compiled for previousstudies (Hapke et al., 2013a; Hapke et al., 2013b; Lentz and Hapke,2011a) and all known, available data were incorporated into the linearrate calculation. Twenty-two surveys of shoreline position, spanning1933 to April 2005 and five surveys of dune toe position from 1998to 2005 were included in change rates. Four additional surveys wereconducted between 2005 and 2009 and the data through July 2009were incorporated into the 2009 dataset linear rate calculation.Given that the historic shorelines and dune toe positions were obtainedfrom a variety of data sources, including T-sheets, GPS surveys, andorthophotos, uncertainty of the data is variable with the source. How-ever, DSAS reports a change rate along with uncertainty of the LRRbased on the number of measurements available at each transect andthe sources of those measurements. Shoreline and dune toe LRR uncer-tainty is reflected in the binning of our shoreline and dune toe linearregression rates (Tables 1A; 1B).

3.1.3. Anthropogenic influenceRecords of nourishment activities on Fire Islandwere compiled from

contractor and U.S. Army Corps of Engineers reports for two previousstudies (CP&E, 2009; Gravens et al., 1999; Kratzmann and Hapke,2012; Lentz and Hapke, 2011a). While the records indicate at leastone nourishment event for all transects, much of the eastern area hasnot been modified since the designation as a National Seashore in1962. A large nourishment project, involving approximately1.4 × 106 m3 of dredged material, took place in the western and centralregions of the island just two months prior to the July survey (Lentzet al., 2013). For this study, nourishment data were organized into inde-pendent event counts then divided by the years since the most recentevent. The nourishment index (NI) is designed to emphasize locationswhere nourishment occurs often aswell asmost recently. It is importantto note that the event counts are based on the best available informationand contain uncertainty due to missing records.

3.1.4. Morphologic changeMorphologic change is used here to describe the observable varia-

tion in shoreline position and beach volume over the study period.NSM was calculated as the horizontal difference between surveyedshoreline positions (Fig. 4H). The NSM parameter represents the shore-ward or landward lateral migration of the MHW shoreline and isreferenced to the offshore baseline. The observed BVC (Fig. 4I) is the dif-ference of beach volumes between survey dates. Uncertainty of theshoreline and beach volume is a function of resolution of the data sourceand interpolation errors associated with extraction of the morphologicfeatures. Volume calculations also integrate vertical uncertainty of topo-graphic data. Bin boundaries (Tables 1A; 1B) were selected to balanceuncertainty with the number of observations in each bin.

Table 1AIndividual parameter bin boundaries for Nor'Ida specific models.

Model parameter Bin boundary values

Wave impact hours (hours) 0 1 10 20 30 100 200 400Run-up elevation (m) 1.9 2.25 2.35 2.5 2.75 3 5Beach width (m) 5 35 50 65 80 110Initial volume (m3/m) 0 30 70 110 150 250Shoreline linear regression rate (m/year) −2.3 −1.1 −0.5 0.1 0.7 1.9Dune toe linear regression rate (m/year) −4.5 −1 0 1 2 5.5Nourishment index 0 0.1 0.25 1 12 35Net shoreline movement (m) −55 −30 −10 0 18 60Beach volume change (m3/m) −200 −75 −50 −25 0 10 50 105

Table 1BIndividual parameter bin boundaries for generalized models.

Model parameter Bin boundary values

Run-up elevation (m) 1.9 2.25 2.5 2.75 3 5Beach width (m) 0 10 20 35 50 65 110Initial volume (m3/m) 0 30 50 70 110 150 250Shoreline linear regression rate (m/year) −2.3 −1.1 −0.5 0.1 0.7 1.9Dune toe linear regression rate (m/year) −7 −3 −1 0 1 2 5 7.75Nourishment index 0 0.1 0.25 0.35 0.5 1 12 35Net shoreline movement (m) −65 −35 −20 −10 0 15 50Beach volume change (m3/m) −200 −100 −25 0 25 100 200

36 K.E. Wilson et al. / Coastal Engineering 102 (2015) 30–43

3.2. Accuracy and model evaluation

Following Bayes Rule, posterior probability is the conditional proba-bility of the forecast variable given the observations of all model param-eters. The bin with the highest posterior probability is compared to theobservations from the hindcast to evaluate model accuracy and can bevisualized in a contingency table. The rows and columns in a contingen-cy table display the discretized intervals of data for the geomorphicresponse variable. The columns show the number of transects predictedin each bin whereas the rows show the number of observations per bin.Ideally, the central diagonal from top left to bottom right will be popu-lated with accurate predictions.

Two additional metrics, skill and log likelihood ratios, were calculat-ed to evaluate model predictions (Fienen et al., 2013; Gutierrez et al.,2011; Palmsten et al., 2014; Plant and Holland, 2011; Plant andStockdon, 2012). Skill depends on the regression between observationsand BN predictions and is calculated by:

s ¼ 1−σ2

e

σ2f; ð4Þ

where σe2 is the mean square error between observations and predic-

tions of morphologic change (BVC or NSM) and σf2 is the variance of

the BVC or NSM observations. Discretization of continuous data in BNnodes reduces the highest achievable skill from 1.0 and the “check”,calculated when values for the forecast variable are provided to themodel, represents the best possible skill for our model binning andstructure. The log likelihood ratio (LLR) is evaluated at the predictionlocations using:

LLRi ¼ log pi FijOj! "

ΔFi¼Δ F j

h i− log pi Fið ÞΔ Fi¼Δ F j

h i: ð5Þ

The first term is the log of the updated conditional probability for thebin that includes the observed morphologic change. The second term isthe log of the prior probability for the same bin. LLR values greater thanzero result when the updated probability, p(Fi|Oj), is higher than theprior, p(Fi), reflecting an improvement in the accuracy of the probabilitydistribution. A summary LLR for eachmodel type is presented in Results.The log ratios presented in the results have been summed over allobservations to reflect the total improvement of the prediction overthe prior probability distribution of the target variable, morphologicchange.

Variance reduction (VR) percent was used to demonstrate sensi-tivity of prediction to each of the model parameters. VR is defined asthe expected change of the posterior probability of a selected parameter,for example NSM or BVC, given the finding at an input variable (Norsys,2010). Percent of VR is calculated using:

VR ¼ V Fið Þ−V FijOj! "

=V Fið Þ& '

" 100; ð6Þ

where V(Fi) is the variance of the prior forecast variable and V(Fi|Oj)is the variance of the posterior forecast variable when updated withobservations. Variance of the prior and posterior are calculated using:

V Fið Þ ¼XN

i¼1

p f ið Þ f i−E f ið Þð Þ2; ð7Þ

and

V FijOj! "

¼XN;M

i; j¼1

p f ijoj! "

f i−E f ijoj! "! "2

; ð8Þ

where p( fi) is the probability of the forecast, p( fj|oi) is the probabilityof the forecast given the observations,( fj) is the observed value of theforecast variable, E( f ) is the expected value of the forecast variable andE( fj|oi) is the expected value of the forecast variable, given the observa-tions. Variance of posterior and prior are summed over N, the numberof bins in the forecast variable, and over M, the number of bins in theobservations (Fienen et al., 2013; Norsys, 2010).

4. Results

Model results are assessed across forecast variable and type, gener-alized or Nor'Ida specific, using accuracy, skill, and log likelihood ratios(Table 3). Although, no model was absolutely the most successfulaccording to these metrics, BVC-G is the most accurate (81.9%) andhas the highest LLR (221). These values for accuracy and skill metricsindicate that the model frequently predicted the observed bin, and theaverage posterior probability was 22% greater than the prior, reflectinghigher confidence in the prediction. Fig. 7 demonstrates the increase inprobability in BVC-G from the prior distribution (A) to the updated,alongshore probability (B). The warm colors indicate the bin with thehighest predicted probability and accurate hindcasts are visualized atlocations where the observed change (black cross) corresponds withthe highest probability in (B). Despite reporting the lowest skill (0.37)of the five models, BVC-G, along with NSM-G, is expected to be amongthe most transferable models to other storm events or locations, basedon the generalized bin distribution and training.

The contingency matrix for BVC-G (Table 2) displays the number ofobservation locations at which the model accurately predicted theobserved bin in the central diagonal, from the top left to the bottomright, and the number of locations at which the model predicted an

Table 2Contingency table for BVC-G.

Predicted beach volume change (m3/m)

−200 to −100 −100 to −25 −25 to 0 0 to 25 25 to 100 100 to 200

30 5 0 0 0 0 −200 to −100 Observed beach volume change(m3/m)6 529 15 1 3 0 −100 to −25

0 69 139 1 2 0 −25 to 01 23 18 37 6 0 0 to 250 10 7 4 27 0 25 to 1000 1 0 0 0 0 100 to 200

Table 3Model results and metrics.

ModelID

Description Accuracy(%)

Error(%)

Skill Log likelihoodratio

NSM-N Nor'Ida run-up 79.0 21.0 0.41 195NSM-G Generalized run-up 73.1 26.9 0.49 206BVC-N1 NOR'IDA run-up 74.9 25.1 0.51 216BVC-N2 Nor'Ida WIH 65.0 35.0 0.41 204BVC-G Generalized run-up 81.9 18.1 0.37 221

37K.E. Wilson et al. / Coastal Engineering 102 (2015) 30–43

incorrect outcome. The values to the left or below the central diagonalindicate themodel predicted a binwith values less than the observation(false-negative), while above the diagonal indicates the values of thepredicted bin were greater than the observation (false-positive). Themajority of BVC-G incorrect predictions were false-negatives (Table 2).

NSM-Nwas 79% accurate and produced skill = 0.41 and LLR= 195.The generalized form of the net shoreline movement model (NSM-G)produced lower accuracy (73.1) but skill improved to 0.49 and LLR to206. The highest skill (0.51) was produced by the BVC-N1 and a LLR of216 represents approximately 21% increase of the posterior probabilityover the prior. BVC-N1 had moderate accuracy (75%) but had a 10%accuracy improvement over the alternative Nor'Ida specific BVC modelwhich incorporated WIH. BVC-N2, reported among the lowest valuesfor each metric; accuracy was just 65%, skill = 0.41, and LLR = 204.

Skill was evaluated when the model was informed with the targetvariable (“check”) (Fig. 8) and when individual parameters were re-moved from model structure. The check represents the best possibleskill for the model, which is theoretically 1.0 but discretization of thedata into bins reduces the best skill to approximately 0.9 in our models.Removing the NI resulted in large decrease in skill across both NSM andBVC model types (Fig. 8). The average reduction of skill when nourish-ment is not included is 12.4%, with the maximum reduction (0.22)in NSM-G. In the four models which utilized the run-up wave parame-terization, removal of beach width resulted in the least reduction ofskill. In three of these models, NSM-N, BVC-G, and BVC-N1, removal ofinitial volume equals the skill when beach width is removed. However,when BVC-G was tested without either initial condition, beach width

nor initial volume, skill (0.21) and LLR (152) were the lowest of anymodel evaluation. BVC-N2, the only model to utilize wave impacthours, demonstrated no reduction of skill (0.41) when the wave pa-rameter was removed (Fig. 8). Alternatively, removal of run-up fromNSM-G, NSM-N, BVC-G, and NSM-N1 resulted in skill reduction of0.11, 0.09, 0.05, and 0.10, respectively. Average skill reduction is 10.6%when shoreline LRR is removed from the model and 10.4% when dunetoe LRR is removed.

Variance Reduction (VR), the expected change of the posterior prob-ability of the predicted variable, given the finding at an input variable(Norsys, 2010), was calculated for each model parameter (Fig. 9). VRpercent is highest for the initial conditions, beach width (0.19) and ini-tial volume (0.23), in BVC-N2. Average values for beach width (0.04)and initial volume (0.04) in the remaining models indicate that thepredictions are consistently sensitive to these parameters. The waveparameter in BVC-N2, wave impact hours, is the least influential in themodel, while run-up reports among the highest VR in NSM-N (0.05)and is relatively high in the other models which utilize R2 as the hydro-dynamic forcing (Fig. 9).

5. Discussion

This study is the successor to the foundational work by Lentz andHapke (2011a), which developed models to hindcast the net shorelinemovement and beach volume change attributable to two storms, thePatriot's Day Storm (2007) and Nor'Ida (2009), at two study sites atFire Island. The models developed by Lentz and Hapke (2011a) included

Fig. 7. Alongshore probability distributions and data for BVC-G. The changes in color along the vertical axis at each alongshore sample location corresponds to the probability of the dataexisting in one of the five bins. A. The prior probability distribution of the data in each bin is uniform alongshore. B. The calculated posterior probability distributions reflect the updatedmodel prediction and vary between alongshore locations. Coincidence of the observed BVC (black cross) with the warmest color in B indicates an accurate prediction. The color bar limitsare adjusted to the highest probability predicted by the model, 0.65.

38 K.E. Wilson et al. / Coastal Engineering 102 (2015) 30–43

long-term rates of change, initial conditions, andwere driven by a param-eterized wave impact value. Model accuracy ranged from 70 to 82%.

We consider this study to represent an improvement upon the pre-vious work because of three important advancements. First, to build onthe work of Lentz and Hapke (2011a) we trained the models with amore robust dataset to represent and make predictions for the fulllength of Fire Island. Spatial expansion of the observational datasetenhances the effectiveness of probabilistic modeling by increasing thenumber of scenarios used to train themodel. Second, the BNs presentedhere incorporate anthropogenic modification through inclusion of thenourishment index. The impact of human intervention is particularlyimportant to consider on Atlantic coast barrier islands, because somany are frequentlymanipulated by human development and engineer-ing practices (Nordstrom, 1994; Nordstrom, 2004). The third advance-ment is the reformulation of our wave parameter and adjustment ofour model structure. Given the probability distributions of each waveparameter, the models are statistically more sensitive to maximumrun-up elevation thanWIH resulting in improvedmodel skill and predic-tive accuracy.

5.1. Sensitivity analysis

5.1.1. Anthropogenic modificationWhen testing the skill reduction, the models without the nourish-

ment node report among the lowest skill across both NSM and BVCmodel structures (Fig. 8). The reduction of skill when nourishment isnot included averages 12.4%, supporting the hypothesis that includinghuman intervention is important to modeling system behavior. VR per-cent for the NI is relatively low across the model iterations; however,

the parameter has the third highest VR percent in BVC-G. Comparedto the othermodels, nourishmentwould be expected to have the largestimpact on predictive ability in BVC-G, given that themodel is formulat-ed to predict volumetric change, impacted by nourishment, and istrained with data bracketing two large replenishment events on the is-land. These events are reflected in higher NI values for 2009 (Fig. 4A).The volumetric change models specific to Nor'Ida (BVC-N1, BVC-N2)are less sensitive to the NI because data collected in 2005, prior to thetwo nourishment events, was not used in training the models. Low VRin the shoreline position models (NSM-G, NSM-N) is likely due to thedegrading influence of nourishment on shoreline position with time,particularly when compared with beach volume.

5.1.2. Wave parameterizationTwo representations of wave forcing were used in the models pre-

sented here. The first, wave impact hours, was used in the foundationalmodel by Lentz and Hapke (2011a) and therefore was initially incorpo-rated into model development, as a control. The use of wave impacthours was originally developed for use on high relief coasts (Ruggieroet al., 2001) and was demonstrated to be an influential parameterin successfully predicting cliff retreat (Hapke and Plant, 2010), butour results indicate that the use of WIH in probabilistic modeling ofbarrier island morphodynamics should be reconsidered. Althoughmodel skill for BVC-N2 (0.41)was comparable to the remainingmodels,accuracy was much lower (65%), and there is no reduction in modelskill when WIH is removed from the model structure (Fig. 8). Further,VR percentage (Fig. 9) demonstrates that the WIH parameter has theleast influence on the ability to hindcast volume change, underscoringthe need to represent waves differently in the model. In contrast

Fig. 8. Comparison ofmodel skill across the fivemodel types and parameters. The best possible skill (black) is calculatedwhen the values for the target variable are provided to themodel.Nor'Ida hindcast skills are shown by the second bar (dark gray) in eachmodel group. The remaining bars demonstrate model skill when one parent variable is removed from themodel.The change in skill when a particular variable is removed indicates the relative importance of the parent in successful prediction of the target variable.

39K.E. Wilson et al. / Coastal Engineering 102 (2015) 30–43

maximum run-up has large reduction in skill when it is removed andrelatively high VR percent across all model types.

Since the WIH parameterization is a direct comparison of total waterlevel and beach morphology, the hydrodynamics in both WIH and run-up models are calculated using the Stockdon et al. (2006) parameteriza-tion. The comparison to the beach morphology in the WIH calculationbecomes important because water levels during our study period rarelyexceed the maximum elevation of the beach. Therefore many observa-tions forWIH result in a value of 0, which is problematic in the BN formu-lation presented here. The values for the parent node, WIH, indicate thatwave collision at themaximumbeach elevation did not occur but suggestthat impact did not occur anywhere on the beach. These values are an in-correct representation of the system and generate a highly skewed prob-ability distribution in thewave forcing (Fig. 6E). Alternatively, discretizingthemaximumrun-up elevation intomore uniformly distributed bins pro-vides adequatenumber of observations in each bin to compute joint prob-abilities (Plant and Holland, 2011) and generates a more accuraterepresentation of wave impact. This is achieved by resolving small differ-ences in water level which can produce large differences in alongshoregeomorphic change. This binning difference, although utilizing the samehydrodynamics and beach slope, could be responsible for the increasedsensitivity to the run-up elevation in the newly structured models.

5.1.3. Historical rates of change and initial conditionsRemoval of shoreline and dune toe linear regression rates (LRR)

results in large reduction in model skill across all model types. Averageskill reduction is 10.6% when shoreline LRR is removed from the modeland 10.4% when dune toe LRR is removed. Linear regression rates cap-ture processes which occur on larger temporal and spatial scales thanother network parameters. Large scale processes, including long-shore

and cross-shore sediment transport and underlying geologic controls,play a role in short and long term evolution of the barrier island. Otherauthors (Palmsten et al., 2014; Plant and Stockdon, 2012) donot includelong term rates of change in their model formulations, but the skill re-duction of our models indicates that these variables are importantwhen hindcasting change over a lengthy observation interval.

The nodes containing initial conditions of beach width and volumeare consistently influential in model predictions and have the highestVR percent in all three BVC models and NSM-G (Fig. 9). The initialconditions are particularly influential in BVC-N2; the VR value for initialvolume is eleven times greater than wave impact hours. However, anunderstanding of the system behavior suggests that the increase in rel-ative sensitivity of the other variables, including long term trends andwave climate, as experienced in the updated model structure is advan-tageous. The relatively small reduction in skill when either beach widthor initial volume is removed (Fig. 8) could indicate redundancy in thetwo variables, which is supported by much greater skill and LLR reduc-tion when both variables are removed and high R2 values betweenbeach width and initial volume for both datasets (2005 0.70; 2009,0.88).

5.2. Model limitations

The LLR (221) and skill (0.37) values for our best model (BVC-G) in-dicate that continued improvement is possible. We recognize that thereare processes such as aeolian and longshore sediment transport, andunquantifiable human activity captured within the timescale of ourdatasets that cannot be explicitly accounted for in a model structure.This ultimately limits model ability. Further, the hindcast models pre-sented here were trained with either one (NSM-N, BVC-N1, BVC-N2)

Fig. 9. Percent of variance reduction formodel variables. Higher values of VR percent indicate greater influence in the prediction of the target variable. NSMand BVC are not shownbecauseby definition the VR percent would be 100%. Beach width and initial volume are consistently high across all model types, while BVC-N2 demonstrates the relatively low influence ofWIH.

40 K.E. Wilson et al. / Coastal Engineering 102 (2015) 30–43

or two (NSM-G, BVC-G) casefile(s) of input parameters, including theobserved change from Nor'Ida. Future work will evaluate the successof volume change probabilistic models when training is expanded toinclude additional storms and a variation of time scales. Increased com-plexity of training datasets is expected to strengthen BN hindcast abilityand improve both LLR and skill metrics.

We also acknowledge two important differences between the 2005and 2009 datasets which likely influenced model performance. First,the 2005 survey period spanned April to November, while 2009 surveyswere collected in July and December. The late spring and early summermonths are recognized as times of beach recovery, when limited waveimpact results in wide, gently sloping beaches (Tanksi, 2007; Wrightand Short, 1984). We suggest that the few months of continued recov-ery between April and July surveys may have played a role in the mor-phologic differences captured by the datasets (Fig. 4D; E).

Of greater importance are two nourishment projects completedbetween 2005 and 2009, one of which occurred only a few monthsprior to our study period. Despite this project being represented in theNI, it resulted in wider initial beach widths and greater initial volumesevident in the 2009 dataset (Fig. 10). Considering that BVC and NSMmodels are highly sensitive to beach width and initial volume (Fig. 9)the dissimilarities between the 2005 and 2009 beach morphology, pro-duced by natural and anthropogenic forces, could be in part responsiblefor the reduced ability to hindcast change in 2009 using 2005 data.

5.3. Applications of BNs in coastal systems

Observation-based probabilisticmodeling has the potential to be ap-plied to a diverse set of coastal research questions. Coastal managers,tasked with identifying zones of greatest vulnerability and allocatinglimited resources, can benefit from the unique characteristics of BNs.The probabilistic predictions generated by BNs are familiar, given thefrequent use of probabilities in weather forecasting, to scientists andnon-scientists alike, and provide a range of predicted outcomes ratherthan an exact “line in the sand”. BNs can also be quickly compiled andupdated with new observations, strengthening future predictions ofmorphologic change. Additionally, quantitative and qualitative data,

such as presence or absence of dune erosion or relative amount ofinfrastructure damage following a storm, can be incorporated to aid indecision making. Finally, Palmsten et al. (2013) demonstrated thatBNs are transferable to new settings, if there is adequate similarity inthe observational data between study sites. Given the data limitationsthat many coastal managers face, development of generalized BNs thatuse extensive datasets from locations such as Fire Island, NY, Duck,NC, and Assateague, MD (Field Research Facility Coastal Observationsand Analysis Branch, 2004; U.S. Geological Survey Fire Island CoastalChange, 2015; U.S. Geological Survey Publications Data Series, 2015)could provide a valuable management tool.

6. Conclusions

We have presented several meaningful additions to probabilisticforecasting in coastal systems such as volumetric change hindcasts, in-corporation of anthropogenic activity, and application of an improvedwave forcing. This study demonstrates that volumetric change, whichhas received little attention in BN modeling, can be predicted on alarge scale with similar success as shoreline position change.

Despite BVC-G generating the lowest skill (0.37), the model accu-rately predicted change along 81.9% of the island, an improvementof 8.5% over NSM-G. Moreover, volumetric change provides a better un-derstanding of the total system behavior than does shoreline position,suggesting that BVC is a preferable management objective. Both NSM-G and BVC-G are expected to have high potential for transferability todifferent storms and locations based on the use of multiple trainingdatasets and generalized bin distribution, but BVC-G is favored dueto increased accuracy. However, shoreline models, of which both thegeneralized and Nor'Ida specific reported promising model metrics,are a valuable tool when topographic data necessary to derive BVC,are unavailable.

The results of shorelinemovement and volume changemodels dem-onstrate that inclusion of anthropogenic modification is important andstatistically meaningful for accurate representation of the pre-existingbeach state and prediction of morphologic change. Nourishment altersthe beach profile and decreases the hindcast skill by an average of

Fig. 10. Initial beachwidth and volume for (A) 2005 and (B) 2009 datasets. Locations of 2007 and 2009 nourishment deposition sites are shown as black boxes, highlighting the increasedvolume and beach width in these areas.

41K.E. Wilson et al. / Coastal Engineering 102 (2015) 30–43

12.4% when disregarded in model formulation. We have shown thatutilizing a maximum run-up elevation improves hindcast accuracyand skill by 10% over a temporal summation of storm impact (WIH).The manner in which hydrodynamics are represented is important ina probabilistic framework due to binning considerations and the needto discretize observational data into approximately even probability dis-tributions. These advancements are shown to improve our ability topredict beach change using probabilistic models and are a valuablecomplement to existingmethods to anticipate risk in vulnerable coastalzones.

Acknowledgments

The authors are grateful for contributions from the following indi-viduals: N. Plant generously offered discussion and code to calculateresults, in addition to a USGS internal review. R. Henderson preparedmany of the historical data for use in this application. S. Vitousek provid-ed a thoughtful review of the original manuscript. The staff of theNational Park Service and Fire Island National Seashore provided logis-tical support and assistance in field operations. We are indebted to thecomments from editors and anonymous reviewers.

References

Aumann, H.H., Ruzmaikin, A., Teixeira, J., 2008. Frequency of severe storms and globalwarming. Geophys. Res. Lett. 35 (19).

Batton, B.K., 2003. Morphologic Typologies and Sediment Budget for the Ocean Shorelineof Long Island, New York. State University of New York at Stony Brook, MarineSciences Research Center, Stony Brook, New York (Ph.D. dissertation).

Bender, M.A., et al., 2010. Modeled impact of anthropogenic warming on the frequency ofintense Atlantic hurricanes. Science 327 (5964), 454–458.

Bruun, P., 1983. Beach scraping — is it damaging to beach stability. Coast. Eng. 7 (2),167–173.

Chen, S.H., Pollino, C.A., 2012. Good practice in Bayesian network modeling. Environ.Model. Softw. 37, 134–145.

Church, J.A., et al., 2013. Sea level change. In: Stocker, T.F., Qin, D., Plattner, G.-K., Tignor,M., Allen, S.K., Boschung, J., Nauels, A., Xia, Y., Bex, V., Midgley, P.M. (Eds.), ClimateChange 2013: The Physical Science Basis. Contribution of Working Group I tothe Fifth Assessment Report of the Intergovernmental Panel on Climate Change.Cambridge University Press, Cambridge, United Kingdom and New York, NY, USA.

CP&E, 2009. 2009 Fire Island beach Renourishment Project Post-Construction Report(37 pp.).

Danforth, W.W., Thieler, E.R., 1992. Digital Shoreline Analysis System (DSAS) User'sGuide, Version 1.0: U.S. Geological Survey Open-File Report 92-355. p. 42.

Davis, R.A., Hayes, M.O., 1984. What is a wave-dominated coast? Mar. Geol. 60 (1–4),313–329.

Elsner, J.B., et al., 2008. The increasing intensity of the strongest tropical cyclones. Nature455 (7209), 92–95.

Emanuel, K., 2005. Increasing destructiveness of tropical cyclones over the past 30 years.Nature 436 (7051), 686–688.

Field Research Facility Coastal Observations and Analysis Branch SandyDuck '97 CoastalField Experiment. (http://www.frf.usace.army.mil/sandyduck/SandyDuck.stm andreferences therein).

Fienen, M.N., et al., 2013. Bridging groundwater models and decision support with aBayesian network. Water Resour. Res. 49, 6459–6473.

Geist, E.L., Parsons, T., 2006. Probabilistic analysis of tsunami hazards. Nat. Hazards 37,277–314. http://dx.doi.org/10.1007/s11069-005-4646-z.

Gravens, M.B., et al., 1999. Fire Island Inlet to Montauk Point Reformulation Study (FIMP):Historical and Existing Condition Coastal Processes Assessment. Prepared for the U.S.Army Engineer Districts, New York.

Grezio, A., et al., 2010. A Bayesian procedure for probabilistic tsunami hazard assessment.Nat. Hazards 53 (1), 159–174.

Guisan, A., Zimmermann, N.E., 2000. Predictive habitat distribution models in ecology.Ecol. Model. 135 (2–3), 147–186.

Gutierrez, B.T., et al., 2011. A Bayesian network to predict coastal vulnerability to sea levelrise. J. Geophys. Res. 116, F02009. http://dx.doi.org/10.1029/2010JF001891.

H. John Heinz Center for Science, Economics, and the Environment, 2000. The HiddenCosts of Coastal Hazards: Implications for Risk Assessment and Mitigation. IslandPress, Washington, D.C.

Haneberg, W.C., 2000. Deterministic and probabilistic approaches to geologic hazardassessment. Environ. Eng. Geosci. 6 (3), 209–226.

Hapke, C.J., Plant, N.G., 2010. Predicting coastal cliff erosion using a Bayesian probabilisticmodel. Mar. Geol. 278 (1–4), 140–149.

Hapke, C.J., et al., 2010. A review of sediment budget imbalances along Fire Island,New York: can nearshore geologic framework and patterns of shoreline changeexplain the deficit? J. Coast. Res. 26 (3), 510–522.

Hapke, C.J., et al., 2013a. Geomorphic and human influence on large-scale coastal change.Geomorphology 199, 160–170.

Hapke, C.J., et al., 2013b. Coastal Change from Hurricane Sandy and the 2012–13 WinterStorm Season—Fire Island. U.S. Geological Survey Open-File Report 2013-1231,New York (37 p., Books and Open-File Reports Section, distributor, Reston, Va).

Harley, M.D., Ciavola, P., 2013. Managing local coastal inundation risk using real-timeforecasts and artificial dune placements. Coast. Eng. 77, 77–90.

Houser, C., 2013. Alongshore variation in the morphology of coastal dunes: implicationsfor storm response. Geomorphology 199, 48–61.

Jaquet, O., et al., 2006. DEVIN: a forecasting approach using stochastic methods applied tothe Soufriere Hills Volcano. J. Volcanol. Geotherm. Res. 153 (1–2), 97–111.

Kana, T.W., 1995. A mesoscale sediment budget for Long Island, New York. Mar. Geol. 126(1–4), 87–110.

Kana, T.W., et al., 2011. Lack of evidence for onshore sediment transport from deep waterat decadal time scales: Fire Island, New York. J. Coast. Res. Spec. Issue 59, 61–75.

Kelley, J.T., 2013. Popham Beach, Maine: an example of engineering activity that savedbeach property without harming the beach. Geomorphology 199, 171–178.

Komar, P.D., Allan, J.C., 2008. Increasing hurricane-generated wave heights along the U.S.East Coast and their climate controls. J. Coast. Res. 24 (2), 479–488.

Kratzmann, M.G., Hapke, C.J., 2012. Quantifying anthropogenically driven morphologicchanges on a barrier island: Fire Island National Seashore, New York. J. Coast. Res.28 (1), 76–88.

Lancieri, M., Zollo, A., 2008. A Bayesian approach to the real-time estimation ofmagnitudefrom the early P and S wave displacement peaks. J. Geophys. Res. Solid Earth 113(B12).

Larranaga, P., Moral, S., 2011. Probabilistic graphical models in artificial intelligence. Appl.Soft Comput. 11 (2), 1511–1528.

Leatherman, S.P., 1985. Geomorphic and stratigraphic analysis of Fire Island, New York.Mar. Geol. 63 (1–4), 173–195.

Lentz, E.E., Hapke, C.J., 2011a. Geologic framework influences on the geomorphology of ananthropogenically modified barrier island: assessment of dune/beach changes at FireIsland, New York. Geomorphology 126 (1–2), 82–96.

Lentz, E.E., Hapke, C.J., 2011b. The Development of a Probabilistic Approach to ForecastCoastal Change, Coastal Sediments, Miami, FL. p. 14.

Lentz, E.E., et al., 2013. Improving understanding of near-term barrier island evolu-tion through multi-decadal assessment of morphologic change. Mar. Geol. 337,125–139.

Leonard, L., et al., 1990. An analysis of replenished beach design parameters on UnitedStates coast barrier islands. J. Coast. Res. 6 (1), 15–36.

Loureiro, C., et al., 2013. Applicability of parametric beach morphodynamic state classifi-cation on embayed beaches. Mar. Geol. 346, 153–164.

Magliocca, N.R., McNamara, D.E., Murray, A.B., 2011. Long-term, large-scale morpho-dynamic effects of artificial dune construction along a carrier island coastline.J. Coast. Res. 27 (5), 918–930.

Marzocchi, W., et al., 2004. Phenomenological evidence in favor of a remote sensingcouple for large volcanic eruptions. Geophys. Res. Lett. 31, L04601.

Melillo, J.M., et al., 2014. Climate change impacts in the United States: the third nationalclimate assessment. U.S. Global Change Research Program http://dx.doi.org/10.7930/J0Z31WJ2 (841 pp.).

National Oceanographic and Atmospheric Administration, Department of Commerce,2012. Storm Surge and Coastal Inundation: Event History. http://www.stormsurge.noaa.gov/event_history.html.

National Oceanographic and Atmospheric Administration, Environmental ModelingCenter, 2015. NWW3 Data Access. ftp://polar.ncep.noaa.gov/pub/history/waves.

Nebel, S.H., et al., 2013. Tropical cyclone frequency and barrier island erosion rates, CedarIsland, Virginia. J. Coast. Res. 29 (1), 133–144.

Nordstrom, K.F., 1994. Beaches and dunes of human-altered coasts. Proc. Phys. Geogr. 18,497–516.

Nordstrom, K.F., 2004. Beaches and Dunes of Developed Coasts. Cambridge UniversityPress, New York.

Nordstrom, K.F., McCluskey, J.M., 1985. The effects of houses and sand fences on theaeolian sediment budget at Fire Island, New York. J. Coast. Res. 1 (1), 39–46.

Norsys, 2010. Netica. www.norsys.com, Ver. 4.16.Palmer, T.N., Ralsanen, J., 2002. Quantifying the risk of extreme seasonal precipitation

events in a changing climate. Nature 415 (6871), 512–514.Palmsten, M.L., et al., 2013. Velocity estimation using a Bayesian network in a critical-

habitat reach of Kootenai River, Idaho. Water Resour. J. 49, 5863–5879.Palmsten, M.L., et al., 2014. Probabilistic estimation of dune retreat on the Gold Coast,

Australia. Shore Beach 82 (4), 35–43.Patenaude, B., et al., 2011. A Bayesianmodel of shape and appearance for subcortical brain

segmentation. NeuroImage 56 (3), 907–922.Plant, N.G., Holland, K.T., 2011. Prediction and assimilation of surf-zone processes using a

Bayesian network part I: forward models. Coast. Eng. 58 (1), 119–130.Plant, N.G., Stockdon, H.F., 2012. Probabilistic prediction of barrier-island response to

hurricanes. J. Geophys. Res. 117, F03015. http://dx.doi.org/10.1029/2011JF002326.Plant, N.G., et al., 2010. Forecasting hurricane impact on coastal topography. Eos 91 (7), 2.Psuty, N.P., Silveira, T.M., 2009. Trend in foredune crestline displacement, Fire Island

National Seashore, New York, USA, 1976–2005. J. Coast. Res. 15–19.Ruggiero, P., et al., 2001. Wave runup, extreme water levels and the erosion of properties

backing beaches. J. Coast. Res. 17 (2), 407–419.Ruggiero, P., et al., 2006. Probabilistic shoreline change modeling. Proceedings from the

30th International Conference on Coastal Engineering, San Diego, CA, September2006.

Sallenger, A.H., 2000. Storm impact scale for Barrier Islands. J. Coast. Res. 16 (3),890–895.

Schwab, W.C., et al., 2000. Influence of inner-continental shelf geologic framework on theevolution and behavior of the barrier-island system between Fire Island Inlet andShinnecock Inlet, Long Island, New York. J. Coast. Res. 16 (2), 408–422.

42 K.E. Wilson et al. / Coastal Engineering 102 (2015) 30–43

Schwab, W.C., et al., 2013. Geologic evidence for onshore sediment transport from theinner continental shelf: Fire Island, New York. J. Coast. Res. 29 (3), 526–544.

Sparks, R.S.J., 2003. Forecasting volcanic eruptions. Earth Planet. Sci. Lett. 210 (1–2), 1–15.Stewart-Koster, B., et al., 2010. The use of Bayesian networks to guide investments in flow

and catchment restoration for impaired river ecosystems. Freshw. Biol. 55 (1),243–260.

Stockdon, H.F., et al., 2006. Empirical parameterization of setup, swash, and runup. Coast.Eng. 53 (7), 573–588.

Tanksi, J., 2007. Long Island's Dynamic South Shore: A Primer on the Forces andTrends Shaping Our Coast (New York Sea Grant. file:///G:/papers/Tanski_2007_LongIslandsDynamicSouthShore_150dpi_11-08-07.pdf).

Thieler, E.R., et al., 2009. The Digital Shoreline Analysis System (DSAS) Version 4.0 — AnArcGIS Extension for Calculating Shoreline Change.

Thompson, C.M., Frazier, T.G., 2014. Deterministic and probabilistic flood modeling forcontemporary and future coastal and inland precipitation inundation. Appl. Geogr.50, 1–14.

Tolman, H.L., 2014. User Manual and System Documentation of WAVEWATCH III Version4.18. NOAA/NWS/NCEP/MMAB. Technical Note 316 (194 pp.).

U.S. Geological Survey, 2014a. Coastal Change Hazards: Hurricanes and Extreme StormsNor'Ida: Pre- and Post-Storm Photo Comparisons — Introduction. U.S. GeologicalSurvey (http://coastal.er.usgs.gov/hurricanes/norida/).

U.S. Geological Survey, 2014b. National Assessment of Shoreline Change Project. http://coastal.er.usgs.gov/shoreline-change/, (and references therein).

U.S. Geological Survey, 2015a. Fire Island Coastal Change. http://coastal.er.usgs.gov/fire-island/.

U.S. Geological Survey, 2015b. USGS Publication Warehouse. http://pubs.er.usgs.gov/browse/usgs-publications/DS/ (and references therein).

Wells, J.T., McNinch, J., 1991. Beach scraping in North Carolinawith special reference to itseffectiveness during Hurricane Hugo. J. Coast. Res. (Special Issue 8).

Wright, L.D., Short, A.D., 1984. Morphodynamic variability of surf zones and beaches: asynthesis. Mar. Geol. 56, 93–118.

Yates, M.L., Le Cozannet, G., 2012. Brief communication “Evaluating European CoastalEvolution using Bayesian Networks”. Nat. Hazards Earth Syst. Sci. 12, 1173–1177.

Zhang, K., et al., 2005. Quantification of beach changes caused during Hurricane Floydalong Florida's Atlantic Coast using airborne laser surveys. J. Coast. Res. 21 (1),123–134.

43K.E. Wilson et al. / Coastal Engineering 102 (2015) 30–43