Exploring vulnerability of coastal habitats to sea level rise through global sensitivity and uncertainty analyses

Environmental Modelling & Software 26 (2011) 593e604

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Environmental Modelling & Software journal homepage: www.elsevier.com/locate/envsoft

Exploring vulnerability of coastal habitats to sea level rise through global sensitivity and uncertainty analyses M.L. Chu-Agor a, R. Muñoz-Carpena a, *, G. Kiker a, A. Emanuelsson a, I. Linkov b a b

Agricultural and Biological Engineering Department, University of Florida, PO Box 110570, Gainesville, FL 32611-0570, United States US Army Engineer Research and Development Center, Concord, MA 01366, United States

a r t i c l e i n f o

a b s t r a c t

Article history: Received 20 January 2010 Received in revised form 1 December 2010 Accepted 2 December 2010 Available online 5 January 2011

Changes in coastal habitats brought about by climate change have the potential to cause population decline of shoreline dependent organisms. In particular, sea level rise associated with climate change can drastically affect wetlands and beaches which are important foraging and nesting areas of these organisms. SLAMM 5 (Sea Level Affecting Marshes Model) is widely used to simulate wetland conversion and shoreline modification for the purpose of habitat vulnerability assessment and decision making, but concerns regarding the suitability of the model due to the uncertainty involved in selecting many of the model’s empirical input parameters have been expressed. This paper applies a generic evaluation framework consisting of a state-of-the-art screening and variance-based global sensitivity and uncertainty analyses to simulate changes in the coastal habitats of the barrier island in Eglin Air Force Base, Florida in order to: (1) identify the important input factors and processes that control SLAMM 5’s output uncertainty; (2) quantify SLAMM 5’s global output uncertainty and apportion it to the direct contributions and interactions of the important input factors; and (3) evaluate this new methodology to explore the potential fate of the coastal habitats of the study area. Results showed that four input factors (DEM vertical error for the lower elevation range, historic trend of sea level rise, accretion, and sedimentation rates) controlled 88e91% of SLAMM 5’s output variance in predicting changes in the beach habitat of Eglin Air Force Base. The most dominant processes governing the fate of the coastline of the study area were inundation (i.e. reduction in elevation due to sea level rise) and accretion/sedimentation. Interestingly, for lower elevation habitats (salt marsh, tidal flat, and beach), results showed possible gain or loss of these habitats depending on the relative strength of these processes resulting from the combination of input factors within their proposed uncertainty ranges. Higher-elevation habitats (swamps and inland fresh marsh) showed decrease in area over 100 years of simulation. These findings are important to implement managerial schemes in the area to protect threatened Plover birds (Charadrius sp.) communities. This generic model evaluation framework is model-independent and can be used to evaluate a wide range of environmental models. Ó 2010 Elsevier Ltd. All rights reserved.

Keywords: Global sensitivity analysis Global uncertainty analysis Fate of coastal habitats Charadrius sp SLAMM 5 Plover habitats Model evaluation

1. Introduction Sea level rise associated with climate change can drastically affect wetlands and beaches that are important foraging and nesting areas for shoreline dependent birds (Fujii and Raffaelli, 2008; Hughes, 2004). As sea level rises, coastal habitats are inundated, eroded, or washed away which can result in habitat lost (Mander et al., 2007; Norris et al., 2004: Pye and Blott, 2006) and in turn cause a decline in the population of these shoreline dependent organisms (Daniels et al., 1993; Fujii and Raffaelli, 2008; Galbraith

* Corresponding author. Tel.: þ1 352 392 1864x287; fax: þ1 352 392 4092. E-mail address: carpena@ufl.edu (R. Muñoz-Carpena). 1364-8152/$ e see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.envsoft.2010.12.003

et al., 2002; Hughes, 2004; Yates et al., 1996). In addition to sea level rise, human activities, along with urbanization can also contribute to population decline (Burger, 1987; Lott, 2008; Thomas et al., 2003). Considering all these factors, the population of shoreline dependent birds are thus constantly being threatened which has stimulated efforts towards conservation and restoration. Given uncertainty in future climate change scenarios and models as well as variability in local conditions, making sound environmental management decisions is a challenge. To support environmental management decisions, an integrated modeling framework is required. This consists of a model to simulate habitat changes linked to a meta-population model that simulates the population of a particular organism based on the projected habitat changes, and further linked with management decision analytics.

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The habitat model SLAMM 5 (Sea Level Affecting Marshes Model) (Warren Pinnacle Consulting, Inc., Warren, VT), developed in the 1980s with the Environmental Protection Agency (EPA) funding, has been used to simulate changes in coastal habitats due to sea level rise in order to assess the future of numerous wetland areas in the United States (Galbraith et al., 2002, 2003; Lee et al., 1991, 1992; NWF, 2006; Park et al., 1991, 1993). However, these studies have not evaluated the effects of uncertain model inputs despite the fact that uncertainties in these inputs were acknowledged as limitations to the results of the analysis (Craft et al., 2009a,b). The uncertainty involved in selecting many of the model’s empirical inputs has raised concerns regarding the validity and suitability of the model. Most of the input factors in SLAMM 5 are based on user expertise which brings the question of how this may affect the output of the model. Another source of uncertainties comes from the use of thematic input maps. These habitat models rely heavily on remotely sensed information which is confronted by methodological challenges, data limitations, classification errors, and uncertainties that may vary from case to case (Castilla and Hay, 2007; Cherrill and McClean, 1995; Dendoncker et al., 2008; Guofan and Wu, 2008; Hines et al., 2005; Keith et al., 2009; Shao and Wu, 2008). In addition to these concerns, the model itself can include conceptual uncertainties, i.e., uncertainty in model structure, assumptions, and specifications (Saltelli et al., 2008). Craft et al. (2009a) investigated the effects of accelerated sea level rise on the tidal marsh along the Georgia coastline. They used SLAMM 5 to predict changes in the area in response to mean and maximum estimates of sea level rise in the year 2100. Their results showed a decrease of 20% in the area of salt marsh for the mean sea level rise and a decrease of 45% for the maximum. Although the methodology used in their study provided important insights on how sea level rise might affect tidal marshes, they acknowledged some limitations in their approach. Specifically, there exist some uncertainties in their input data which have not been quantified as well as uncertainties involved in the scaling of laboratory and plot measurements to landscape level. In addition to this, the structure of SLAMM 5 does not consider feedback mechanisms among variables which may happen as sea level rises. Kirwan and Guntenspergen (2009) pointed that the lack of stated uncertainty in data inputs in Craft et al. (2009a) study can limit the usefulness of the model results for planning or management purposes. In their response, Craft et al. (2009b) acknowledged the need to perform uncertainty analysis in future studies. Uncertainties in a model cannot be avoided since uncertainty is not an accident of the scientific method, but rather its substance (Saltelli et al., 2008). Knowing the uncertainties in the model’s input and how they may affect model outputs will help ensure the reliability of these outputs, and thus build confidence in the model. This is especially crucial if the model is used to estimate the impact of human actions on natural resources and to interpret the significance of those effects in light of the uncertainties identified in each component of the evaluation process (Cariboni et al., 2007). Furthermore, understanding the sensitivity of the model to the different input factors and the interactions among them will augment our understanding of the system and the important processes producing changes in the habitats or in other environmental systems under specific conditions. In addition, sensitivity and uncertainty analyses can identify factors which greatly influence the variability of the model’s outputs for the purpose of prioritizing data collection and research, and for model verification and validation (Frey et al., 2004). This paper applies a generic (i.e., model-independent) evaluation framework to assess the vulnerability of the coastal habitats of the barrier island in Eglin Air Force Base, Florida due to sea level rise. Since this generic framework is model-independent, it can be

applied to many environmental modeling problems beyond its application in this study. This approach employs state-of-the-art screening and variance-based global sensitivity and uncertainty analyses (Saltelli et al., 2005) for SLAMM 5 in order to: (1) identify the important input factors and processes that control SLAMM 5’s output uncertainty; (2) quantify SLAMM 5’s global output uncertainty and apportion it to the direct contributions and interactions of the important factors; and (3) evaluate this new methodology to explore the vulnerability of the coastal habitat of the study area. This paper is the first part of a series of papers that will integrate habitat and meta-population models to be used as a basis for management-related efforts to protect endangered coastal bird communities. 2. Materials and methods 2.1. The study area SLAMM 5 was applied to a part of the Eglin Air Force Base (AFB) coastline near Pensacola, Florida (Fig. 1). Coastal military installations in the southeastern United States like Eglin have significant coastal habitats which are sanctuaries to shoreline dependent birds. Specifically, Snowy Plover (Charadrius melodus) and wintering Piping Plovers (Charadrius alexandrines) were documented to have nesting areas within Santa Rosa Island, a barrier island along the base’s southern shore. However, there are concerns about the effects of military training activities (e.g. amphibious landings) and future infrastructure projects (e.g. access road armouring, dune and shoreline re-nourishment, creation of seawalls and bulkhead) in the area to these habitats and to the birds’ population itself. Recent projections of habitat loss for shoreline dependent birds at important coastal sites in the U.S. range between 20% and 70% (Galbraith et al., 2002). This is particularly alarming for Snowy and Piping Plovers which are considered threatened species (Brown et al., 2001; Lott, 2008; USFWS, 1996, 2003). Moreover, Lott (2008) documented the presence of the Snowy Plover in the Florida panhandle specifically within areas that were uninhabited or un-restored. This is a confirmation of earlier studies that man’s activities tend to drive these birds away (Burger, 1987; Thomas et al., 2003). These factors, in conjunction with sea level rise have the potential to increase pressure on the population of these threatened bird species in the study area. 2.2. SLAMM 5: general concepts SLAMM 5 simulates the dominant processes involved in coastal wetland conversions and shoreline modifications during long-term sea level rise. Inundation (i.e. reduction in elevation due to sea level rise), erosion, overwash, saturation, and accretion are the primary processes included in SLAMM 5. The model can simulate 23 different wetland categories based on the National Wetland Inventory (Clough, 2008). Each wetland type is associated with certain elevation boundaries (Fig. 2) and conditions (e.g. salinity, tidal ranges, etc.) required for that specific wetland type to exist. SLAMM 5 divides a spatial area into square cells of customized size and carries out the calculations for each cell, determining whether the cell is going to remain in the same category, or be converted to another. Conversion of a cell to another wetland type is generally governed by the minimum elevation of that cell which is given as follows: MEt ¼ MEt1 þ DtðARÞ  SLRt

(1)

where ME is the minimum cell elevation, AR is the site-specific accretion and/or sedimentation rate, SLR is the sea level rise, and t is the time. Sedimentation refers to deposition of eroded and weathered mineral sediments on the beach and tidal flat. Accretion refers to the increase in marsh surface elevation from sedimentation plus organic matter accumulation from plant biomass. Sea level rise is estimated at each time step as:
 SLRt ¼ GSLRt þ ðtn  t0 Þ risetrendlocal  risetrendglobal

(2)

where GSLR is the global average sea level rise predicted based on particular growth scenarios, tn is the current model year, t0 is the initial year, risetrendlocal is the local historic trend of sea level rise, and risetrendglobal is the global historic trend of sea level rise. In general, the fate of the wetland is determined by the ME of the cell compared to the elevation boundaries of the wetland category it belonged to. If the ME of the cell is lower than the lower boundary of that wetland category, a fraction of that cell will be converted to another wetland category of lower elevation. The fraction of the cell lost (i.e. converted to another wetland class) is computed as follows:
FLt ¼

LBMEt tan a

W

 (3)

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Fig. 1. The Eglin AFB coastline and the Santa Rosa barrier island (Florida, USA) where population of Snowy Plovers and Piping Plovers were documented (FWC, 2010). Global sensitivity and uncertainty analyses of SLAMM were performed on a portion of the Santa Rosa barrier island (enclosed in a box). where FLt is the fraction of wetland in the cell lost at time t, LB is the lower boundary of the wetland category, a is the slope of the cell, and W is the width of the cell. For cells adjacent to the water, additional fraction may be lost due to erosion if the erosion threshold set by the model is exceeded. Additional cell fraction lost, FLE, due to erosion is given as:

FLE;t ¼ Dt



 ER W

(4)

where ER is the site-specific erosion rate specified by the user. Input data in SLAMM 5 consist of the elevation, slope, land cover, site-specific information (e.g. erosion rate, accretion rate, storm frequency, etc), and sea level rise (SLR) scenarios. Output from SLAMM 5 is a simulated land cover in time. 2.3. Application of SLAMM 5 to Eglin AFB

Fig. 2. SLAMM inundation model showing the general elevation hierarchy of the wetlands and their boundaries where MLW is the mean low water heights observed; MTL is the datum located midway between the mean of high water and the mean of low water heights observed; MWHinland is the mean of inland high water heights relative to MTL; and MWHSinland is the mean of high water heights when the moon’s gravitational effect causes water to be on its highest (after Clough, 2008).

Prior to applying SLAMM 5 to the Eglin AFB, data were collected from different open source databases. Slope and elevation data were obtained from the 2005 post Katrina USACE survey (USACE, 2009) with a vertical accuracy of 0.20 m. This data set, which has a lower accuracy, was used to represent a conservative, worst case scenario. If DEM error were found to be important through this analysis, its actual contribution to output uncertainty would then not be greater than what is reported here. On the other hand, if DEM error were found to be unimportant, this would imply that better accuracy in the data would not improve the uncertainty of the output. Land cover maps on the other hand, were obtained from the National Wetland Inventory (USFWS, 2009). Since NWIeGIS layers only display wetlands, all other land types such as beach and developed areas, were displayed as no data. This posed a problem in SLAMM 5 since calculations cannot be performed on cells that do not have data. To address this, cells without data were assumed to be estuarine beach cells. Although SLAMM 5 simulation was carried out for the entire coastal area, evaluation of results was focused on a portion of the barrier island (see Fig. 1) only since the interest (i.e. foraging and nesting areas of Snowy and Piping Plovers) of this study is located in these beach areas. Considering this, converting the no-data cells to estuarine beach cells was a reasonable assumption. The entire study area was divided into cells of 30  30 m. The 30-m cell size was used since if SLAMM 5 is run with a cell size of less than 30 m, the overwash portion of the model does not handle the barrier islands properly in its default formulation (J.S. Clough, personal communication, September 17, 2009). Twenty-seven input parameters of SLAMM 5 were initially defined (Table 1). This consisted of site-specific inputs, elevation data, land cover data, and slope. With the global sensitivity and uncertainty analyses in mind, the elevation grid was divided into five zones (Table 1) in order to distribute errors in the DEM data into five elevation ranges. This was necessary since DEM errors were recognized to manifest spatial variability and dependence (Darnell et al., 2008). This division is parallel to

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Table 1 Input factors for SLAMM and assumed statistical distributions for the global and sensitivity analyses. No.

Input factors

Description

Units

Value

Distributionb

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27

Elevzone1 Elevzone2 Elevzone3 Elevzone4 Elevzone5 Wetltype3 Wetltype5 Wetltype8 Risetrend Tidalrange Tidalrangeinl Mhws Marshero Swampero Tiflaero Samaaccre Bramaaccre Tifreaccre Sedratebeach Stormfrq Maxfethres Maxwiow Owbeoc Owdrbe Owesbe Owmarperlo Owmangperlo

DEM vertical error (0e1 m) DEM vertical error (1e2 m) DEM vertical error (2e3 m) DEM vertical error (3e4 m) DEM vertical error (4e5 m) Wetland type (Swamp) Wetland type (inland fresh marsh) Wetland type (salt marsh) Historic trend of sea level rise Tidal range at site (vertical) Tidal range inland Mean high water spring Marsh erosion Swamp erosion Tidal flat erosion Salt marsh vert. accretion Brackish marsh vert. accretion Tidal fresh vert. accretion Beach/tidal flat sedimentation rate Frequency of large storms Max fetch threshold Max width of overwash Overwash beach to ocean Overwash dryland to beach Overwash estuary to beach Overwash marsh percent loss Overwash mangrove percent loss

m m m m m e e e mm/yr m m m horiz. m/yr horiz. m/yr horiz. m/yr mm/yr mm/yr mm/yr mm/yr yr/overwash km m m m m % %

0.2 0.2 0.2 0.2 0.2 3 5 8 2.10 0.35 0.35 0.5235 2.0a 1.0a 0.2a 7.0e8.0 3.0e4.0a 4.0a 3.9e8.6 2 9a 500a 30a 30a 60a 50a 25a

U(0.2, 0.2) U(0.2, 0.2) U(0.2, 0.2) U(0.2, 0.2) U(0.2, 0.2) D (5, 3, 8) D (3, 5, 8) D (3, 8, 5) T(1.5, 2.1, 2.4) U(0.35, 0.383) U(0.35, 0.383) U(0.464, 0.575) U(1.6, 2.4) U(0.8, 1.2) U(0.16, 0.24) T(0.9, 3.2, 8) U(3, 4) U(3.2, 4.8) T(0.01, 1.456, 5) DU(1, 2, 3) U(7.2, 10.8) U(400, 600) U(24, 36) U(24, 36) U(48, 72) U(40, 60) U(20, 30)

a

Default values from SLAMM. Assumed distributions and their parameters: U ¼ uniform distribution (left boundary, right boundary); D ¼ discrete distribution (discrete value1, discrete value2, discrete value3) where the probability for each value is (0.025, 0.95, 0.025), respectively; T ¼ triangular distribution (minimum, peak, maximum); DU ¼ discrete uniform distribution (discrete value1, discrete value2, discrete value3). b

SLAMM 5’s wetland hierarchy (Fig. 2) that depends on elevation, while maintaining the spatial structure (e.g. physiographic features like dunes, flats, etc.) within each elevation range. Three wetland categories, swamp (3), inland fresh marsh (5), and salt marsh (8) were considered as input factors to account for possible errors in land cover classification (e.g. classifying it as wetland category 3 or 8 when in fact it is 5, etc.). Output from SLAMM 5 used in this study consisted of cell counts of the barrier island (island) and of the five wetland/coastal habitats that comprised it (Fig. 2), namely: swamp, inland fresh marsh, salt marsh, tidal flat, and beach. Sea level rise (SLR) was simulated using the Intergovernmental Panel on Climate Change (IPCC, 2001) A1B scenario. To account for the variation in estimates of sea level rise, SLAMM 5 was simulated using “model’s minimum,” “model’s average,” and “model’s maximum” results as published in that document (IPCC, 2001). These were referred to in this paper as minimum, mean, and maximum SLR scenarios. The initial simulation time was set to 2001 as this corresponded to the latest NWI photo date. The simulation period was 2001e2100 although outputs were considered for 2060 and 2100 only. The year 2060 is specifically important since it was reflected in the growth scenario for Florida based on “Florida 2060 report” (Zwick and Carr, 2006). 2.4. Global sensitivity and uncertainty analyses In general, uncertainty analysis propagates the uncertainties in the model’s inputs to its outputs while sensitivity analysis determines the contribution of each input factor to the uncertainty of the outputs. Uncertainty and sensitivity were evaluated using a two-step global sensitivity and uncertainty analyses (GSA) method: the screening method proposed by Morris (1991) and a variance-based technique proposed by Sobol (1993). The Morris method provides a qualitative assessment of the importance of each input factor while the Sobol method performs a quantitative analysis of sensitivity and uncertainty. This two-step methodology has been used in recent studies of inputeoutput relationship and model evaluation (Fox et al., 2010; Jawitz et al., 2008; Muñoz-Carpena et al., 2007, 2010). The Morris method is composed of individually randomized input factor designs. The data analysis was based on the resulting random sample of observed elementary effects, i.e., those changes in an output due solely to changes in a particular input (Morris, 1991). Each input may assume a discrete number of values, called levels that are selected within an allocated range of variation for the parameter. The number of simulations, N, required to perform the Morris analysis is given as: N ¼ rðk þ 1Þ

(5)

where k is the number of input factors, and r is the sampling size for each trajectory (r ¼ 10 produces satisfactory results as suggested by Campolongo et al., 2007). For

each parameter, two sensitivity measures can be calculated: (1) the mean elementary effect, m, and (2) the standard deviation of the elementary effects, s. The former estimates the overall effect of the parameters on a given output while the latter estimates the higher-order characteristics of the parameters, such as curvatures and interactions. Because the model output can be non-monotonic, Campolongo et al. (2007) suggested considering the distribution of the absolute values of the elementary effects, m* to avoid the cancelling effects of opposing signs. Although elementary effects are local measures, the method is considered global because the final measure, m* is obtained by averaging the elementary effects. This averaging eliminates the need to consider the specific points at which they are computed (Saltelli et al., 2005). Interpretation of the results is carried out by plotting s on the vertical axis and m* on the horizontal axis for each input factor. Qualitative input factor importance for a given output can be visually assessed in the (m*, s) plane based on the horizontal distance from the origin (m*-coordinate), while the presence of interactions is indicated by the vertical separation from the origin (s-coordinate). Since the Morris method is qualitative in nature, it should only be used to identify the important input factors which drive model’s output uncertainty and assess their relative ranking. A variance-based method like Sobol (1993) has the capacity to quantify the influence of the full range of variation of each input factor as well as the interaction effects among the input factors (Saltelli et al., 2008). Sobol generalized the variancebased method proposed by Cukier et al. (1978) and provided a straightforward Monte Carlo-based implementation of the concept, capable of computing sensitivity measures for arbitrary groups of factors (Saltelli et al., 2008). For variance-based sensitivity analysis methods, the first-order sensitivity index, Si, represents the main effect (direct) contribution of each input factor to the variance of the output. It is expressed as: Si ¼

Vi V

(6)

where Vi is the part of the variance due to the input factor Xi, and V is the total variance of the model output. Sobol’s variance decomposition can investigate the interaction (higher-order effects) between input factors producing a given effect on a particular output. The total effect index, STi, which is the result of the variance decomposition, accounts for the total contribution to the outputs variation due to factor Xi, i.e. its first-order effect plus all the higher-order effects due to interactions (Saltelli et al., 2008). For example, for three input factors X1, X2, and X3, the STi of factor, X1 can be expressed as: ST1 ¼ S1 þ S12 þ S123

(7)

where ST1 is the total sensitivity index of X1, S1 is the main effect of X1, S12 is the interaction effect between X1 and X2, and S123 is the interaction effect between X1, X2,

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Prior to performing GSA, the pdfs of the 27 input factors were defined (Table 1) based on values from open form databases, literature review, and default values of SLAMM 5. Discrete distributions were used for categorical data like wetland type based on SLAMM 5’s classification (i.e., 3 ¼ swamp, 5 ¼ inland fresh marsh, 8 ¼ salt marsh) assuming 5% error that each wetland type was incorrectly classified. The storm frequency (stormfrq) was assigned a uniform discrete distribution based on the frequency of storm for the last ten years in the area (i.e., 1, 2, or 3 years/overwash) (NOAA, 2009b). The historic trend of sea level rise (risetrend) (NOAA, 2009a) and salt marsh vertical accretion rate (samaaccre) manifested minimum, maximum and most likely values along the coast of the Gulf of Mexico and were assigned triangular distributions (DeLaune et al., 1992). Beach/tidal flat sedimentation rate (sedratebeach) was also assigned triangular distribution based on data from Lee (1982). Uniform distributions (with a range of 20% from the base value) were assigned to input factors when only the base value was known, the range was considered finite, and no explicit knowledge of the distribution was available (McKay, 1995). This conservative assumption allows an equal probability of occurrence of the input factors along the probability range (Muñoz-Carpena et al., 2010). The base value for the DEM vertical error (elevzone1e5) was chosen based on the known vertical accuracy of the DEM data of 0.2 m (metadata from digital coast, http://www.csc. noaa.gov). This error was used to simulate a conservative, worst case scenario since the actual DEM error for the entire map must be less than this value. The results can therefore overestimate the actual output uncertainty due to DEM error. Uniform distributions were also used for the tidal range at the site (tidalrange) (NOAA, 2009a), tidal range inland (tidalrangeinl) (NOAA, 2009a), and mean high water spring (mhws) (NOAA, 2009a), based on data obtained for the Pensacola, Florida region. The rest of the input factors were assigned uniform distributions based on SLAMM default values (Table 1).

the results of the minimum, mean, and maximum SLR scenarios. For screening comparison purposes, the five habitat types (map area extent) were grouped together based on the SLAMM 5 inundation model (Fig. 2) into higher elevation (swamp and inland fresh marsh) and lower elevation (salt marsh, tidal flat, and beach) wetlands. The segregation between these two groups was defined by the salt boundary (Fig. 2). Only lower elevation wetlands serve as foraging and nesting habitats for Florida Snowy and Piping Plovers (Convertino et al., in press; Pruner, 2010; Nicholls and Baldassarre, 1990; Gore and Chase, 1989). Higher-elevation wetlands (i.e., swamp and inland fresh marsh) showed identical results and are represented by the swamp habitat in the following discussions. Results for the tidal flat were similar to those for the beach and were therefore not shown unless deviations were observed. In general, higher-elevation wetlands were found to be sensitive to DEM vertical error for the lower elevation range zone of 0e1 m (elevzone1) and historic trend of sea level rise (risetrend) for both 2060 and 2100 mean SLR scenario (Fig. 3a and b). These results were consistent with the conceptual theory behind SLAMM 5 since the fate of the wetland was determined by the minimum elevation (ME) of the category (cell) computed using the cell elevation (equation (1)) and the estimated SLR which in turn was a function of risetrend (equation (2)). For lower elevation wetlands on the other hand, salt marsh vertical accretion rate (samaaccre) and/or beach/tidal flat sedimentation rate (sedratebeach) outweighed the effects of elevation (Fig. 3cef). Accretion/sedimentation rates (samaaccre and sedratebeach) became more important as a result of further reduction in elevation brought about by SLR. This can be due to the fact that as SLR continues to increase, retention of a particular cell within a given category is only possible through accretion or sedimentation (see equation (1)). Also for lower elevation wetlands, risetrend and samaaccre acted as interactive factors as indicated by their vertical deviation from the origin of the m*es plot. Furthermore, results indicated that for the lower elevation wetlands, the number of important factors increased. This signified that for these wetlands, the variance in the output is driven by more factors than that of the higher-elevation wetlands adding complexity to the model. Minimum and maximum SLR scenarios showed parallel results for higher-elevation wetlands (Fig. 4a and b). This is an implication that for these wetland categories, outputs were less sensitive to variation in the estimates of sea level rise. Lower elevation habitats (Fig. 4cef) on the other hand were more sensitive to SLR scenarios as suggested by changes in rankings of the important input factors between the minimum and maximum values. As the SLR assumed the maximum value, sedimentation and accretion became important. The important factors in both the minimum and maximum SLR scenarios were in general the same although their rankings were changed. The results from the Morris screening method reduced the 27 input factors to an overall total of 11 important input factors (Table 2). These important factors were consistent across the three SLR scenarios studied although some of the ranks were interchanged in some wetland types.

3. Results and discussion

3.2. Variance-based sensitivity analysis results

3.1. Screening by Morris method

Using only the 11 input factors, the variance-based uncertainty and sensitivity analyses were carried out to further quantify the effects of these inputs on the outputs. A total of 61,440 (12,288 for sensitivity analysis and 49,152 for uncertainty analysis) simulations for each SLR scenario were required by the Sobol method. The Si indices (Table 3) numerically assessed the main effect contribution of each input factor to the variability of the output (Table 3). For

and X3. Using equation (7), subtracting S1 from ST1 provides a measure of how much X1 is involved in interactions with any other input factors (Saltelli et al., 2008). The sum of all Si is equal to 1 for additive models and less than 1 for non-additive models. P The difference 1  Si can be used an indicator of the presence of interactions in the model (Saltelli et al., 2008). The number of simulations required for Sobol method is given as: N ¼ ð2k þ 2ÞM

(8)

where M is the sample size (typically taken between 500 and 1000). Since Sobol method uses a randomized sampling procedure, it can be used as a basis for global uncertainty evaluation by constructing the probability distribution functions (pdf) and cumulative distribution functions (cdf) for each of the selected outputs. This could lead to an efficient Monte Carlo type of uncertainty analysis, if only the sensitive factors identified by the Morris screening method are considered as the source of uncertainty (Muñoz-Carpena et al., 2007). Application of the screening method involved five steps: (1) the probability distribution functions for each input factor were selected; (2) sample points were generated from the distributions using the Morris method; (3) SLAMM 5 was executed using each of the sample points and a set of outputs was generated; (4) global sensitivity analysis was performed; and (5) important input factors were identified and examined in the variance-based analysis. By considering only the important input factors, the variance-based analysis was carried out following the same steps 1e4 of the Morris method except that sample points were generated using the Sobol method (step 2). Global sensitivity and uncertainty analyses were then performed by computing Si, STi, STi  Si and constructing the pdfs and cdfs of the SLAMM 5 outputs (i.e., changes in the surface area of the coastal habitats). SimLab (Version 2.2) software designed for Monte Carlo-based uncertainty and sensitivity analyses (Saltelli et al., 2004) was used to analyze the model results employing the Morris and Sobol methods. For each SLR scenario, SLAMM 5 was executed with 280 Morris simulations (following equation (5)), 12,288 Sobol simulations for sensitivity analysis, and 49,152 Sobol simulations for uncertainty analysis. Due to the computational cost involved in running the Sobol method, the sample size required was first determined by generating different sample sizes (i.e. different values of M in equation (8)) until convergence was reached. Simulations were carried out at the High Performance Computing (HPC) center of the University of Florida (http://hpc.ufl.edu). 2.5. Derivation of input pdfs

The 27 input factors were evaluated qualitatively from the m*es plot (Figs. 3 and 4). The effects of sea level rise were evaluated by first comparing the plots of 2060 to that of 2100 for each wetland category considering the mean SLR scenario. Effects in the variation in the estimates of sea level rise were then evaluated by comparing

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a

b

c

d

e

f

Fig. 3. Results of the Morris method for (a and b) swamp (example of a high-elevation wetland), (c and d) salt marsh, and (e and f) beach (low-elevation wetlands) showing the important input factors that influence uncertainty in the output based on the mean SLR scenario.

example, 90% of the output variance in salt marsh map extent in 2060 (considering the mean SLR scenario) can be attributed to the direct contribution from samaaccre and 1% from risetrend (the rest were contributions from interactions). In general, higher-elevation wetlands, derived their total variability (95e99%) mostly from elevzone1 while lower elevation wetlands from samaaccre and/or sedratebeach. For the beach, it is interesting to note the dominant contribution of samaaccre (2060 ¼ 62%, and 2100 ¼ 31%) to the variance of the output. This is likely due to the overlap in elevation

boundaries between the beach and salt marsh (Fig. 2). Similarly, salt marsh and tidal flat shared a boundary within the beach category (Fig. 2), hence the influence of samaaccre in the output of the tidal flat (2060 ¼ 74% and 2100 ¼ 64%). For the portion of the barrier island considered in this study (island), output variability was attributed from elevzone1, risetrend, samaaccre, and sedratebeach. Results showed that the most dominant factor in the barrier island is sedratebeach in 2060 (51%) which further became more important in 2100 (61%). As sea level rise accelerated from 2060 to 2100,

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Fig. 4. Results of the Morris method for minimum and maximum SLR scenarios for the year 2100 for (a and b) swamp, (c and d) salt marsh, and (e and f) beach.

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Table 2 Ranking of important input factors after Morris method for the mean SLR scenario. Input factors

Rank Swamp

Inland fresh marsh

Salt marsh

Island

Tidal flat

Beach

2060 Elevzone1 Elevzone2 Risetrend Tidalrange Tidalrangeinl Tiflaero Samaaccre Bramaaccre Tifreaccre Sedratebeach Maxfrethres

1 e 3 e 2 5 6 4 e 7 e

1 e 4 e 3 e e 5 2 e e

2 10 4 8 6 3 1 5 9 7 e

1 7 5 6 9 3 4 10 11 2 8

3 e 4 6 8 5 1 7 e 2 e

2 7 5 6 10 4 1 8 11 3 9

2100 Elevzone1 Elevzone2 Risetrend Tidalrange Tidalrangeinl Tiflaero Samaaccre Bramaaccre Tifreaccre sedratebeach maxfrethres

1 e 2 e 3 6 5 4 e e e

1 5 3 e 4 e e 6 2 e e

3 9 2 10 5 8 1 4 7 6 e

2 10 4 6 9 7 3 8 e 1 5

4 9 3 5 8 6 1 7 e 2 e

3 10 4 6 9 7 1 8 e 2 5

samaaccre, and sedratebeach outweighed the importance of elevzone1 as the ME of the cell continued to decrease also confirming Morris results. The total contribution of the factors to the variability of the outputs was represented by STi. This includes Si and higher-order effects like interaction (see equation (7)). The interaction effects were computed by subtracting Si from STi (Table 3). The difference, STi  Si, measured how much a certain factor is involved in Table 3 Global sensitivity results for SLAMM 5 outputs after Sobol’s method showing the most important input factors that drive output uncertainty. Bold values are contributions/interactions equal to or greater than 5%. Input factors

SLAMM 5 outputs Swamp Inland fresh marsh Salt marsh Island Tidal flat Beach

Sobol first-order indices, Si 2060 Elevzone1 99% 98% Samaaccre 0% 0% Sedratebeach 0% 0% Others 1% 1% Total 100% 99%

0% 90% 0% 1% 91%

38% 3% 51% 6% 98%

1% 74% 24% 1% 100%

8% 62% 20% 1% 91%

2100 Elevzone1 96% Samaaccre 0% Sedratebeach 0% Others 2% Total 98%

95% 0% 0% 4% 99%

0% 91% 0% 3% 94%

16% 17% 61% 5% 99%

1% 64% 19% 1% 85%

7% 31% 47% 2% 87%

Interaction, STi  Si 2060 Risetrend 0% Samaaccre 0% Sedratebeach 0% Others 0%

0% 0% 0% 2%

7% 7% 0% 0%

3% 0% 5% 3%

9% 6% 3% 0%

6% 5% 2% 1%

2100 Risetrend Samaaccre Sedratebeach Others

0% 0% 0% 2%

8% 8% 0% 0%

3% 2% 5% 2%

14% 18% 12% 1%

8% 8% 6% 1%

0% 0% 0% 1%

interactions with any other input factors. For instance, the variance in the area of the salt marsh in 2100 resulted from the direct contributions of samaaccre (91%) and risetrend (2%) and also from an 8% interaction of these factors with all other input factors. This may imply that extreme values of the area of salt marsh are uniquely associated with particular combinations of samaaccre and risetrend with other input factors (Saltelli et al., 2008). In general, the 11 input factors showed limited interactions for the model output studied with the exception of the tidal flat area where risetrend, samaaccre, and sedratebeach exhibited some degree of interactions especially for the 2100 predictions (Table 3). The overall results from GSA suggested that inundation (elevzone1 and risetrend being important input factors) and accretion/ sedimentation were the most important processes affecting the barrier island in Eglin AFB. This conformed to SLAMM 5’s conceptual framework since these factors directly affect the ME (equation (1)) of the cell which in turn determined the fate of the wetlands. The results of the sensitivity analysis were comparable to that of the Morris method. In fact, 84% (10 out of 12) of the factors ranked #1 by Morris method was also ranked #1 in the Sobol method and 50% (6 out of 12) of ranked #2 in Morris was also ranked #2 in Sobol (Tables 2 and 3). The difference between the two methods can be attributed to the difference in the number of SLAMM 5 simulations. It can be recalled that the Morris method generated 280 sample points against Sobol which generated 12,288 samples. Results also justified the use of default input factors from SLAMM 5 (see Table 1) since the outputs were not affected by these factors. However, more efforts should be focused on ensuring the reliability of elevzone1, risetrend, samaaccre, and sedratebeach values or improving the description of their underlying processes. Since no available data for samaaccre was found for the study area, the data from the coast of Louisiana was used because of its proximity to the study area. However, although the Florida panhandle is close to Louisiana, the marshes in our study area are more stable, and do not subside as much as those in Louisiana’s Mississippi River delta. Since results showed that samaaccre is one of the important sources of uncertainty in the model output, it is recommended that future research is conducted to quantify samaaccre for the study area. Also, a more robust analysis focusing on the spatial variability of the DEM error should be considered in future studies given its importance as one of the input factors driving the uncertainty of the output. 3.3. Global uncertainty analysis The global uncertainty analysis provided complementary insights on the range of variability of each output. The effect of sea level rise was evaluated by comparing the pdfs and cdfs of each wetland for 2060 and 2100 (Fig. 5aef). Again, the wetlands were grouped into higher and lower elevation wetlands. It was observed that higher-elevation wetlands exhibited the same variability (Fig. 5a and b). Both years showed the same distribution except that the 2100 pdf was shifted to the left signifying decrease in the area. This is in agreement with SLAMM 5’s theoretical framework where SLR reduces the ME of the cells (equation (1)) and thus converting them to another wetland category of lower elevation (equation (3)). For lower elevation wetlands, however, there were some changes observed in the output pdfs between 2060 and 2100 (Fig. 5cef). Interestingly, salt marsh showed a bimodal distribution, one peak of which suggested an increase in the area while the other peak showed a decrease (Fig. 5c and d). The positive peak in 2060 decreased in 2100 while the negative peak increased. This shifting of peaks can be attributed to the non-linear accelerated rise in sea level as projected by SLR scenario between 2060 and 2100. The bimodality in the output distribution of salt marsh is an indication that there are combinations of the input factors (and their

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Fig. 5. Global uncertainty analysis for the (a and b) swamp, (c and d) salt marsh, and (e and f) beach considering the mean SLR scenario showing the full range of variability in the outputs.

underlying processes) that can actually result in net gain of the surface area. It can be recalled that the variability in salt marsh (Table 3) was attributed to the individual effects of samaaccre (90e91%) and risetrend (1e2%) as well as their interactions (7e8%) with other input factors. These interactions could have created combinations that resulted to salt marsh being lost or gained. The gain in area can be due to higher-elevation wetlands being

converted to salt marsh (i.e. wetland migration or transgression) while the loss is when salt marsh is converted to a tidal flat. The beach also showed some increase in the area in 2060, however, in 2100 it assumed a different distribution showing decline in the area (Fig. 5eef) which indicated conversion to open water. A knowledge of the conditions producing such increase or decrease in the wetland is especially useful in assessing the vulnerability of the

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barrier island and in implementing management alternatives. Additional analyses like Monte Carlo mapping could be performed in order to identify the region of the factor space linked with the management-desired model output (i.e. an increase or decrease in area of the wetland). If these factors can be controlled (e.g. erosion rate), management schemes can be implemented by limiting these factors in order to produce the range of output space needed. Given that our method provides probabilistic information towards the

possibility of habitat loss or gain, managers can use model simulations to explore potential assurance levels of ecosystem performance. For example, managers can explore the acceptability of a potential management action to reduce an 80% habitat loss probability to a more acceptable 5% loss probability. The effects of the different SLR scenarios on model uncertainty were evaluated by comparing the minimum, mean, and maximum pdfs/cdfs of each wetland category from 2100 (Fig. 6aef). In general,

Fig. 6. Global uncertainty analysis for (a and b) swamp, (c and d) salt marsh, and (e and f) beach considering the minimum, mean, and maximum SLR scenario for 2100.

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a more narrow range of variability was observed for the minimum SLR scenario and a wider range for the maximum. This is specifically evident in the lower elevation wetlands (Fig. 6c and d). This implied that as SLR accelerated, more variability is introduced into the output. It was interesting to note that for salt marsh, there was a shift in the peak from positive to negative when the SLR scenario changed from minimum to maximum. This suggests that SLR scenarios play an important role in the fate of salt marsh predictions causing decrease in area. These results are particularly important as bases for managerial schemes. For example, the maximum projected sea level rise scenario results in a decrease of salt marsh and the beach in general, which are important habitats of the Snowy Plovers. This scenario will require conservation efforts to be implemented in order to protect these habitats. In contrast, the minimum sea level rise scenario results in an increase of these habitats that translates into a lesser need for conservation efforts. Given that all scenario simulation results provide explicit probabilities towards the occurrence of habitat areas, systematic risk and decision assessments using these probabilities can then be carried out based on these scenario-based probabilities. It is envisioned that these result will be used within a multiple criteria decision analytic structure as detailed in Kiker et al. (2005) and (2008). 4. Summary and conclusions The variability in the change in area of the higher-elevation wetlands was attributed in general to the DEM vertical error for the lower elevation range zone (0e1 m) (95e99%) and historic trend of sea level rise (1e2%). Interactions between input factors for these wetlands were negligible. Higher-elevation wetland showed a general decrease in area from 2060 to 2100 and from minimum to maximum SLR scenarios. For lower elevation wetlands, the variance in the output was mostly driven by varying percentages of the DEM vertical error for the lower elevation range zone (0e1 m), historic trend in sea level rise, salt marsh vertical accretion, and beach/tidal flat sedimentation rate with the latter two factors outweighing the others. As the elevation of the wetland decreased (due to SLR), the number of factors affecting the variance of the output increased adding complexity to the model outputs. Interactions were observed for historic trend of sea level rise, salt marsh vertical accretion, and beach/tidal flat sedimentation rate which suggested that a unique combination of these factors with other input factors can result in extreme values of the output. This is specifically manifested in the variance of salt marsh which showed a bimodal distribution with one peak suggesting an increase in the area while the other suggesting a decrease. This implies that there exist unique combinations of input factors that can result in salt marsh being lost or gained. The predicted fate of the barrier island in Eglin AFB therefore depends on these unique combinations of input factors. Overall, SLAMM’s output was found to be most sensitive to the DEM vertical error for the lower elevation range zone (0e1 m), historic trend in sea level rise, salt marsh vertical accretion, and beach/tidal flat sedimentation rate. This result was consistent with the model’s theoretical framework since these factors were the main variables which determined the minimum elevation of the cell (i.e., equation (1)) and thus, its fate. This further confirmed that the most important processes involved in the fate of the coastal habitat in Eglin AFB were inundation (reduction in elevation due to sea level rise) and accretion/sedimentation. This study demonstrated that the systematic exploration of the multi-variate input space provided by GSA is critical to identify and understand the dominant processes affecting the changes in coastal habitats. These were otherwise not known by the use of simple evaluation approaches relying on a limited number of simulations around a narrow input variation (e.g. classical one-at-a-time local sensitivity analysis techniques). Understanding these important

603

processes should be a prerequisite before any conservation and restoration efforts take place. Furthermore, GSA was able to reduce the number of model input factors and hence enables researchers to focus on important variables that really affect the system. This generic, model-independent evaluation framework will result in a more efficient use of resources as well as ensure the reliability of the entire modeling process. However, as with any model application, the model output and its evaluation are only as good as the inputs that go into it. Results from this study indicate that accretion/sedimentation and elevation are important input factors that drive output uncertainty are therefore candidates for further model development and evaluation studies. Acknowledgements The authors acknowledge the help of Jonathan S. Clough, Dr. Richard A. Fischer, Dr. Matteo Convertino, and the computational resources and support of the University of Florida High Performance Computing Center (http://hpc.ufl.edu). This effort was sponsored by the U.S. Department of Defense and Strategic Environmental Research and Development Program (SERDP, SI-1699, PI: I. Linkov). Permission was granted by the USACE Chief of Engineers to publish this material. The views and opinions expressed in this paper are those of the individual authors and not those of the US Army, or other sponsor organizations. References Brown, S., Hickey, C., Harrington, B., Gill, R., 2001. United States Shorebird Conservation Plan, second ed. Manomet Center for Conservation Sciences. Burger, J., 1987. Physical and social determinants of nest-site selection in Piping Plover in New Jersey. Condor 89, 811e818. Campolongo, F., Cariboni, J., Saltelli, A., 2007. An effective screening design for sensitivity analysis of large models. Environ. Modell. Softw. 22, 1509e1518. Cariboni, J., Gatelli, D., Liska, R., Saltelli, A., 2007. The role of sensitivity analysis in ecological modelling. Ecol. Model. 203, 167e182. Castilla, G., Hay, G.J., 2007. Uncertainties in land use data. Hydrol. Earth Syst. Sci. 11, 1857e1868. Cherrill, A., McClean, C., 1995. An investigation of uncertainty in field habitat mapping and the implications for detecting land cover change. Landscape Ecol. 10 (1), 5e21. Clough, J.S., 2008. SLAMM 5.0.2 Technical Documentation. Warren Pinnacle Consulting, Inc.. Convertino, M., Elsner, J.B., Muñoz-Carpena, R., Kiker, G.A., Martinez, C.J., Fisher, R.A., Linkov, I. Do tropical cyclones shape shorebird habitat patterns? Biogeoclimatology of Snowy Plovers in Florida. PloS One, in press. Craft, C., Clough, J., Ehman, J., Joye, S., Park, R., Pennings, S., Guo, H., Machmuller, M., 2009a. Forecasting the effects of accelerated sea-level rise on tidal marsh ecosystem services. Front. Ecol. Environ. 7 (2), 73e78. Craft, C., Clough, J., Ehman, J., Joye, S., Park, R., Pennings, S., Guo, H., Machmuller, M., 2009b. SLR and ecosystem services: a response to Kirwan and Guntenspergen. Front. Ecol. Environ. 7 (2), 127e128. Cukier, R.I., Levine, H.B., Shuler, K.E., 1978. Non sensitivity analysis of multiparameter model systems. J. Comput. Phys. 26, 1e42. Daniels, R.C., White, T.W., Chapman, K.K., 1993. Seal-level rise: destruction of threatened and endangered species habitat in South Carolina. Environ. Manage. 17 (3), 373e385. Darnell, A.R., Tate, N.J., Brunsdon, C., 2008. Improving user assessment of error implications in digital elevation models. Comput. Environ. Urban Syst. 32, 268e277. DeLaune, R.D., Patrick Jr., W.H., Smith, C.J., 1992. Marsh aggradation and sediment distribution along rapidly submerging Louisiana Gulf Coast. Environ. Geol. Water Sci. 20 (1), 57e64. Dendoncker, N., Schmit, C., Rounsevell, M., September 2008. Exploring spatial data uncertainties in land-use change scenarios. Int. J. Geogr. Inf. Sci. 22 (9), 1013e1030. Florida beach-nesting birds website (FWC), 2010. Technical Report. Florida Fish and Wildlife Conservation Commission. http://www.myfwc.com/shorebirds/BNB/ data.asp (accessed July 2010). Fox, G.A., Muñoz-Carpena, R., Sabbagh, G.J., 2010. Influence of flow concentration on parameter importance and prediction uncertainty of pesticide trapping by vegetative filter strips. J. Hydrol. 384, 164e173. Frey, H.C., Mokhari, A., Zheng, J., 2004. Recommended Practice Regarding Selection, Application, and Interpretation of Sensitivity Analysis Methods Applied to Food Safety Process Risk Models. Prepared by North Carolina State University for the Office of Risk Assessment and CosteBenefit Analysis. United States Department of Agriculture (USDA), Washington, D.C., 149 pp.

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